Curve through Fixed Point

Because of topographic features or other obstacles, the surveyor may find it necessary to determine the radius of a curve which will pass through or avoid a fixed point and connect two given tangents. This may be accomplished as follows (figure 10):

1. Given the PI and the I angle from the preliminary traverse, place the instrument on the PI and measure angle d, so that angle d is the angle between the fixed point and the tangent line that lies on the same side of the curve as the fixed point.
2. Measure line y, the distance from the PI to the fixed point.
3. Compute angles c, b, and a in triangle COP.
   c = 90 – (d + I/2)
   To find angle b, first solve for angle e
   Sin e = Sin c / Cos I/2
   Angle b = 180°- angle e
   a = 180° – (b + c)
4. Compute the radius of the desired curve using the formula
   R = y Sin c / Sin a
5. Compute the degree of curve to five decimal places, using the following formulas:
   (arc method) D = 5,729.58 ft/R
   D = 1,746.385 meters/R
   (chord method) Sin D = 2 (50 feet/R)
   Sin D = 2 (15.24 meters/R)
6. Compute the remaining elements of the curve and the deflection angles, and stake the curve.