Designing and plotting a curve using field data requires precise calculations and execution. A horizontal curve with a radius of 200 meters and an intersection angle of 20 degrees is established using the method of perpendicular offsets from the long chord. The long chord, which spans between the curve's endpoints, is calculated to be 69.46 meters in length. To maintain accuracy in plotting, intervals of 3 meters are selected along the chord.
The engineer determines the offset distances for each interval using the offset formula. At the midpoint of the chord, the ordinate value is calculated and validated against the middle ordinate formula of the curve, ensuring the curve's design adheres to precise geometric standards.
The long chord is then marked on the ground, with points identified at 3-meter intervals along its length on either side of the midpoint. For each point, the perpendicular offset distance is measured and marked on the ground at a right angle to the chord. The top ends of these offset points represent the curve’s position at specific intervals.
By connecting the upper ends of the offsets smoothly, the curve is created on the ground, adhering to the design specifications. This method ensures the curve is accurately plotted, providing a reliable framework for the project.
Consider that a civil engineer has to plot a simple horizontal curve with a 200-meter radius and a 20-degree intersection angle in the field.
The engineer uses the method of perpendicular offsets from the long chord to plot the curve.
First, the long chord length is calculated as 69.46 meters, and the intervals for perpendicular offsets are set at 3 meters.
Next, the offset expression at the midpoint is used to determine the ordinate of the long chord’s center, and to ensure accuracy, this value is verified against the middle ordinate of the curve.
The engineer marks the long chord of the curve on the ground, and the points at 3-meter intervals along both sides of the midpoint are marked.
Then, the expression for the offset distance is used to calculate the perpendicular offsets, which are marked along the long chord at the corresponding points.
Finally, the engineer connects the top ends of the perpendicular offsets to form the curve.
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