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.

 DEFLECTION ANGLE 32 24 0 VELOCITY = 110 kph RADIUS = 1000 metres INTERSECTION CHG. 1350.468 metres MULTIPLES OF THROUGH CHG. 20 metres RATE OF CHANGE OF RAD. ACC.  q 0.3 m/s3 length of transition 95.093 metres Shift   S 0.377 metres Length of main tangent 338.183 metres distance to first point 7.715 metres chainage to first point 1020 metres Chainage at T 1012.285 metres Chainage at T1 1107.378 metres chainage chord len. y(m) def angles 1012.285 Deg Min Sec 1020.000 7.715 7.715 0.005977 0 0 21 1040.000 20.000 27.715 0.077135 0 4 37 1060.000 20.000 47.715 0.228628 0 13 43 1080.000 20.000 67.715 0.460459 0 27 37 1100.000 20.000 87.715 0.772625 0 46 21 1107.378 7.378 95.093 0.908073 0 54 29