In road and rail construction, horizontal curves are used to smooth the transition when changing direction.

For simple, small radii curves and circular curve is designed.

For larger curves where vehicles and trains are travelling at very high speeds, then compound curves are needed.

A compound curve comprises a start transition, short circular section and finish transition.

A transition curve is used to gradually introduce the centrifugal force experienced when travelling along a circular path at speed.  It begins with an infinite radius which gradually reduces until the radius of the simple circular section is reached.  The following part of the spreadsheet calculates the setting out data for deflection angles of the first transition.  Page 2 and 3 of the spreadsheet completes the circular and final transition sections.

Spreadsheets