Creating a Transition

When you design the alignment supporting the course of the road or railway, you can define horizontal or vertical curves with the support of spiral transition curves. You can create a transition to simulate the natural turning path of a vehicle, taking the centripetal force into account.

This task shows you how to:


Before you begin: The behavior of the horizontal alignment items are illustrated in diagrams below as follows:
  • A transition curve simulating the natural turning path of a vehicle is noted as « S » like spiral.
  • A straight section of the horizontal alignment is noted as « T » like tangent.
  • A circular arc is noted "C".

Context: In road/railway engineering and horizontal alignment design, transition curves are widely used for connecting and transiting the geometry between line segments (tangent) and arcs (circular curves). They are also called Euler spirals, characterized by their curvature being proportional to their length, and the constant rate of change of centrifugal acceleration.

These curves provide gradual transitions from straight to circular curves to enable the driver to ride smoothly by turning the steering wheel with a constant speed, defining a spiral. They must respect particular design rules depending on the road type, speed, and superelevation.

Create a Simple Transition

In the alignment sketcher, you can create a transition between a line (tangent) and a circular arc, or between two lines, or between a tangent and parameters.

  1. To create a transition curve for connecting and transiting the geometry between a tangent and a circular curve, click Transition from the Alignment section of the action bar and, do the following:
    1. Select a type of transition to create for the horizontal or vertical alignment.
    2. Select an Initial geometry: Tangent line at the initial extremity of the transition curve.
    3. Optional: Specify a Start point (useless when final extremity is defined by a circle).
    4. Select a circular arc.
    5. Optional: When initial geometry is a line, select the Reverse option to reverse the orientation of the initial tangent and change the side of the transition curve, and the final tangent orientation (if the geometry is a line). This option is useless when the final extremity is defined by a circle or a point.
    6. Select the Final geometry: Final extremity of the transition curve (a tangent or an arc). You can select the final curve to create this transition curve between two circles in ove (a circle within another circle).
    7. Select the Reverse curve side option to define on which side of its initial oriented tangent the curve will turn.
  2. To create a transition curve fully parametrized, select an origin point of the transition, a normal direction (tangent) to orient it and two parameters out of the five required ones:
    • “A” parameter (LxR=A²)
    • Transition length (L)
    • Arc radius (R)
    • Angle at end point
    • Shifting
      Note:

      Origin point

      Length (L)

      Radius

      Shifting

      End Angle

      In specific cases detailed above, parameters are computed automatically and the parameter frame is grayed out. For example, when the final geometry is a point or an arc, a message appears: no additional parameter is required. And the OK button is available only if all parameters are coherent. If not, an error message is displayed.

    When 2D geometry defines totally or partially the final extremity of the transition curve, the final geometry may be:

    • Null, or a point, line, or circle. If null, both parameter1 and parameter2 are required.
    • A line specifying the tangent at the final extremity of the curve. Then parameter1 is required and cannot be an angle.
    • A point or a circle does not require any additional parameter.

    Tips: To connect 2 lines with a combination of S-C-S, use the Horizontal Curve command available in both the contextual bar after selecting an intersection point and the Sketcher section of the action bar. For more information, see Creating a Horizontal Curve.

    If transition lengths are null, only an arc is created.

    Default values are initialized with minimum values based on the current alignment design rules defined for this alignment. If no minimum values can be retrieved from the design rules, L1=0, L2=0 and radius is automatically computed based on the selected lines.

    You obtain this configuration: a transition between a tangent and an arc (T-S-C).

    Tangent

    First spiral (transition)

    Curve (arc)

    Second spiral (transition)

    Tangent

    The transition is rigid but movable. Sketcher constraints are supported on transition curve such as coincident, fix, tangency and curvilinear distance. Its curvature begins with zero at the straight section (tangent) and increases linearly with its curve length. Where it meets the circular curve, its curvature becomes equal to that of the latter.

  3. Optional: To edit a transition, in the tree, click the transition element and, from the context toolbar, select Edit Geometry Definition .
    The Transition Definition dialog box opens and lets you edit the parameters of the transition.

Create a Clothoid Between Circles in ove

You can create a clothoid between two arcs when they do not intersect each other and follow opposite directions.

  1. From the Alignment section of the action bar, click Transition .
  2. To choose the initial geometry, click either of the arcs.
  3. To choose the final geometry to create the clothoid, select the other arc.

    You obtain this configuration with circles in ove: C-S-C.

    Note: The Cubic Parabola type is not available between two circles.

Create a Clothoid Between Circles Exterior to one Another

You can create a clothoid between two arcs that are exterior to one another, and that follow opposite directions without intersecting.

  1. From the Alignment section of the action bar, click Transition .
  2. To choose the initial geometry, click either of the arcs.
  3. To choose the final geometry to create the clothoid, select the other arc.

    You obtain this configuration: C-S-C. The clothoid (orange) replaces the tangent and is inserted between both arcs (blue):



    Note: The Cubic Parabola type is not available between two circles.