Compound Curves

A curve consisting of two or more arcs of different radii curving in the same direction and having common tangent or transition curve at their point of junction is called compound curves. In other words, a curve that is made up of series of successive tangent circular arcs is called compound curves.

It is difficult to construct a compound curve passing through the points let us consider as A, B, C, D, and E, connects the points by straight lines. The straight line between the each pair of points comprises the chord of the arc through the points.

• Erect a perpendicular bisector from AB. Select an appropriate point 01 on the bisector as a center, and draw the arc AB.
• From 01, draw the radius 01B.
• From BC erect a perpendicular bisector.
• The point of intersection 02 between this bisector and the radius 01B is the center for the arc BC.
• Draw the radius 02C, and erect a perpendicular bisector from CD.
• The point of intersection 03 of this bisector and the extension of 02C is the center for the arc CD.
• To continue the curve from D to E, reverse the direction of curvature.
• Draw the radius 03D, and erect a perpendicular bisector from DE on the opposite side of the curve from the previously erected.
• The point of the intersection of the bisector and the extension of 03D is the centre of the arc DE.

Elements of compound curve

The elements of compound curve is,

• PC = point of curvature
• PT = point of tangency
• PI = point of intersection
• PCC  = point of compound curves
• T₁ = Length of tangent of the first curve
• T₂  = length of tangent of the second curve
• V₁ = vertex of the first curve
• V₂ = vertex of the second curve
• I₁ =  central angle of first curve
• I₂ = central angle of second curve
• I angle of intersection = I₁ + I₂
• L_c1 = length of the first curve
• L_c2 = length of the second curve
• L₁ = length of the first chord
• L₂ = length of the second chord
• T₁ + T₂ = length of common tangent measure from V₁ to V₂
• Θ = 180° – I
• X and Y can be found triangle V₁-V₂-PI
• L can be found from the triangle PC-PCC-PT.

Questions:

• Definition of compound curve?
• What are PC and PT stands for?