Setting Out for Circular Curve

Locating the intersection and tangent points is the first and the most important step during the setting out of circular curve.

After these key points are identified, we can proceed with the setting out of the entire horizontal circular curve using tangential angle method. This is the most accurate method among traditional methods, which also include offsets from either tangent or long chord.

Prior to the setting out, we need to set the chord length and calculate the angle associated with it. The value of chord length should not be greater than R/20, where R is the circular curve radius and it is usually provided by the designer.

One theodolite is often enough to complete the curve setting out process.

During the setting out process, we can obtain the coordinates for tangent points and intersection point. With these information as well as the circular curve design data, we will be able to determine the coordinates for a series of point on curve.

We now have a simple circular with radius of 200m and deflection angle of 21.866 degree. The relevant design data such as tangent length, curve length etc are provided by the designer.

Based on this information, we need to conduct the setting out process. In this example, tangential angle method is implemented for its accuracy. The maximum interval of points is R/20 i.e. 10m to ensure the assumptions for this method are valid. Then, we set the initial and final sub-chord length, so that the intermediate points are exactly at 10m multiples.

For each chord length, we calculate corresponding tangential angle. At this point, we have gathered all the information needed to conduct setting out process using theodolite. However, in this example we are required to work further and determine the coordinates for each point.

We first determine the angle between the straight line connecting the tangent point and each curve point, and the horizontal. Then, we can use the cumulative tangential angle to find the length of that straight line. Once all the data are obtained, we can calculate the relative x and y distance between the curve points and tangent point. This is how we can determine their coordinates.