Calculation example – Road design– Circular arc implementation 2

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, where node K (intersecting point of the two main tangents) is not accessible to occupy.

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

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

Step 1: Define two auxiliary points B and C reciprocally visible along tangents E1 and E2 respectively, and measure length (BC).

Step 2: Measure angles δ₁ and δ₂ and calculate supplementary angles γ₁ and γ₂.

Step 3: Applying sine law on triangle KBC:

Calculate (KB) and (KC):

Step 4: Calculate lengths (KA) and (KT) along tangents by entering known values for angle α and radius R on the following functions:

Step 5: Calculate lengths (BA) and (CT), occupy points B and C and define points A and T respectively:

Step 6: To define arc’s middle point M, apply sine law on triangle BKD and calculate length (BD) along BC line:

Step 7: Define and occupy point D on the ground by measuring length (BD) along direction BC, define angle ω and direction of line KM and finally define middle point M by measuring length (DM) along direction of line KM.