Track transition curve

August 08, 2021

Enter values for the track width (guage), turn radius, angle and how much of the curve is used to transition to from straight to the curve radious.

Uncheck the ease out option if the end of the curve should not transition back to straight.

Length of red line:
Turn size: ×
Save generated SVG image (mm)
Save generated SVG image (inch)


The image is generated as three separate curves after eachother:

  1. An Euler spiral from zero curvature to the curve radius.
  2. A circle arc with the curve radius.
  3. A reversed Euler spiral from the curve radius to zero curvature.

The Euler spirals are scaled to match the curvature to the circle arc where they are connected.


  1. Divide the angle into the three separate curve parts; an Euler spiral, a circle arch and a reversed Euler spiral.
  2. Calculate the length of the first Euler spiral given the angle, then scale it so it ends with the correct curvature.
  3. Draw the Euler spiral using scaled Fresnel S and C integrals.
  4. Draw the circle arc.
  5. If ‘ease out’ is selected, draw the reversed Euler sprial, rotated and translated to the correct possition.


  1. Track transition curve, Wikipedia.
  2. Euler spiral, Wikipedia.
  3. Fresnel integral, Wikipedia.
  4. Power series, Wikipedia.

©2023 Mats Mattsson