What does the formula LC = 2 R sin I/2 calculate?

The formula LC = 2R sin(I/2) is used to calculate the Long Chord of a circular curve, where LC represents the Long Chord, R is the radius of the curve, and I is the central angle in radians that subtends the curve. The Long Chord connects the endpoints of the arc directly and lies along the straight line that spans across the curve, rather than following its curvature.

This formula is derived from the geometry of a circle and the properties of triangles formed by the radius and the long chord. It effectively expresses the relationship between the radius of the curve, the angle subtended by the arc, and the direct distance between the endpoints of that arc. This understanding is vital for surveyors when dealing with circular curves, as knowing the Long Chord allows them to determine important aspects of roadway alignments and design.

In a practical situation, when one needs to find the straight line distance between two points on a circular road, you'd apply this formula. This makes the Long Chord crucial for ensuring accurate measurements and planning in surveying and civil engineering projects.