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.
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