Transition types

The software supports the following transition types.

Method Length End station PI
Clothoid spiral

*

*

*
Egg‑shaped clothoid spiral

*

*

–
Cubic spiral

*

*

*
Bloss spiral

*

*

*
Korean Clothoid and PI

*

 

*
Korean cubic parabola

*

*

*
NSW cubic parabola

*

*

–

The clothoid spiral is defined by the length of the spiral and the radius of the adjoining arc. The formulae for the x and y parameters in terms of these two values are as follows:

Parameter x:

Parameter y:

A parameter:

The clothoid spiral can also be defined by a single value called the A parameter (or clothoid parameter). This method is common in various regions and provides an alternative way to calculate the spiral's geometry.

The relationship between the A parameter, the curve radius, and the curve length is given by the formula:

R*L=A2

R: Curve radius

L: Curve length

A: A parameter (spiral parameter or clothoid parameter)

When defining a horizontal alignment in Trimble Access, a transition definition is available for the Points of Intersection (PI) and Length/Coordinates entry methods when you select the Clothoid spiral as the Transition type. You can choose to define the spiral by its Length (L) or by its A parameter (A). The software then automatically calculates all other values.

By editing the Start / End radius for an Entry / Exit transition from Infinite to a required radius it is possible to define an egg shaped clothoid. To return to an infinite radius, select Infinite from the pop‑up menu.

The cubic spiral is defined by the length of the spiral and the radius of the adjoining arc. The formulae for the x and y parameters in terms of these two values are as follows:

Parameter x:

Parameter y:

Parameter x:

Parameter y:

NOTE – The Bloss spiral can only be fully developed, that is, for an entry transition the start radius is infinite and similarly for an exit transition the end radius is infinite.

The Korean Clothoid is a method using a standard clothoid spiral for defining an alignment with linear concentric stationing. It is defined by the Points of Intersection (PI) method, where the input includes the construction centerline transition lengths and the construction centerline radius. These inputs establish two concentric paths: a surveying centerline and a construction centerline. The Vertical alignment start point can be defined either by the Distance from the start of the horizontal alignment or by the station of the Vertical Intersection Point (VPI).

This cubic parabola is defined by the length of the parabola and the radius of the adjoining arc. The formulae for the x and y parameters in terms of these two values are as follows:

Parameter x:

Parameter y:

NOTE – The Korean cubic parabola can only be fully developed, that is, for an entry transition the start radius is infinite and similarly for an exit transition the end radius is infinite.

The NSW cubic parabola is a special parabola used for rail projects in New South Wales, Australia. It is defined by the length of the parabola and an m value. Refer to NSW Government Technical Note ESC 210 Track Geometry and Stability.