Calculation example – Road design– Circular arc implementation

How to implement on the ground the main components (start, middle, end points) of a circular curve with known radius R, tangent to two main alignments E1 and E2, by occupying node K (intersecting point of the two main tangents).

Known values: Curve radius R, Tangents E1 and E2.

Solution: Positions of main components A, M, T on the ground.

Step 1: Occupy node K and measure angle θ (included angle between main tangents).

Step 2: Calculate supplementary angle α

Step 3: Calculate lengths (KA) and (KT) along tangents and (KM) by entering known values for angle α and radius R on the following functions: 

Step 4: Arc’s length (AMT) is calculated through function:

where:

* gon = gradian