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Compound Curves

Compound curves are horizontal curves in highway and railway engineering that consist of two or more simple circular arcs of different radii, joined together and curving in the same direction, with a common tangent at their point of connection. They are used when site conditions or alignment constraints make a single-radius curve impractical, allowing a smoother transition between tangents while fitting the roadway within limited right-of-way or difficult terrain.

Problem: Length of Common Tangent and Common Chord

Two simple curves are connected together as physical obstructions do not permit the use of a single circular curve. The radius of the first curve is 400m while that of the second is 300m. The angles of intersection of the first and second curves are 36º and 50º, respectively. The stationing of PC is 4+509. Determine the following:
a. Length of the common tangent
b. Stationing of PT
c. Stationing of the vertex
d. Length of the common chord

Highway Engineering – Problem: Length of Common Tangent and Common Chord – Diagram
Highway Engineering – Problem: Length of Common Tangent and Common Chord – Diagram Highway Engineering – Problem: Length of Common Tangent and Common Chord – Diagram Highway Engineering – Problem: Length of Common Tangent and Common Chord – Diagram Highway Engineering – Problem: Length of Common Tangent and Common Chord – Diagram

Problem: Compound Curve where the Common Tangent is Parallel to the Long Chord

The long chord from the PC to the PT of a compound curve is 300 meters long and the angles it makes with the longer and shorter tangents are 12º and 15º respectively. If the common tangent is parallel to the long chord.
a. Find the radius of the first curve.
b. Find the radius of the second curve.
c. If the stationing of PC is 10+204.30, find the stationing of PT.

Highway Engineering – Problem: Compound Curve where the Common Tangent is Parallel to the Long Chord – Diagram
Highway Engineering – Problem: Compound Curve where the Common Tangent is Parallel to the Long Chord – Diagram Highway Engineering – Problem: Compound Curve where the Common Tangent is Parallel to the Long Chord – Diagram

Problem: Compound Curve Given Three Tangents with Respective Azimuths

A compound curve connects three tangents having azimuths of 254º, 270º, and 280º, respectively. The length of the chord is 320m long measured from the PC to the PT of the curve, and it is parallel to the common tangent having an azimuth of 270º. If the stationing of PT is 6+520:
a. Determine the total length of the curve.
b. Determine the stationing of the PCC.
c. Determine the stationing of PC.

Highway Engineering – Problem: Compound Curve Given Three Tangents with Respective Azimuths – Diagram
Highway Engineering – Problem: Compound Curve Given Three Tangents with Respective Azimuths – Diagram

Problem: Compound Curve Given the Length of the Common Tangent and Azimuths | Chord Basis

The common tangent AB of a compound curve is 76.42m with an azimuth of 268º30', the vertex V being inacessible. The azimuths of the tangents AV and VB were measured to be 247º50' and 282º50', respectively. The stationing at A is 10+010.46 and the degree of the first curve is 4º based on the 20m chord. Use chord basis.
a. Compute the stationing of PCC
b. Compute the radius of the second curve
c. Compute the stationing of PT
d. Compute the length of the common chord.

Highway Engineering – Problem: Compound Curve Given the Length of the Common Tangent and Azimuths | Chord Basis – Diagram
Highway Engineering – Problem: Compound Curve Given the Length of the Common Tangent and Azimuths | Chord Basis – Diagram Highway Engineering – Problem: Compound Curve Given the Length of the Common Tangent and Azimuths | Chord Basis – Diagram
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