Design Example: Setting a Curve Using Design Data

The perpendicular offsets method plots a horizontal curve by measuring perpendicular distances from a long chord at regular intervals. The engineer marks the long chord on the ground, identifies points at equal intervals along it, calculates perpendicular offset distances using a formula, and marks these offsets at right angles to the chord. Connecting the offset endpoints creates the curve.

The long chord length is calculated using the curve's radius and intersection angle. For a 200-meter radius curve with a 20-degree intersection angle, the long chord measures 69.46 meters. This chord spans between the curve's endpoints and serves as the reference line for plotting perpendicular offsets.

The middle ordinate is validated to ensure the curve's design adheres to precise geometric standards. The engineer calculates the ordinate value at the chord's midpoint using the offset expression and verifies it against the middle ordinate formula. This validation confirms accuracy before marking perpendicular offsets on the ground.

Points are marked at 3-meter intervals along the long chord on both sides of the midpoint. This interval spacing maintains accuracy in plotting while keeping the number of calculations manageable. Each interval point receives a corresponding perpendicular offset distance calculated using the offset formula.

For each marked point along the long chord, the engineer calculates the perpendicular offset distance using the offset formula. The offset is then measured and marked on the ground at a right angle to the chord. The top ends of these perpendicular offsets represent the curve's position at specific intervals.

After all perpendicular offsets are marked, the engineer connects the upper ends of the offset points smoothly to form the curve on the ground. This creates a continuous curve that adheres to the design specifications, providing a reliable framework for the project.

Appropriate interval spacing balances accuracy with practicality. The 3-meter intervals chosen for this example ensure the plotted curve closely matches the design specifications without requiring excessive calculations. Smaller intervals increase accuracy but demand more field work, while larger intervals reduce effort but may compromise precision.