CIRCULAR CURVES

Circular curves are the most common type of horizontal curve used to connect intersecting tangent (or straight) sections of highways or railroads. In most countries, two methods of defining circular curves are in use: the first, in general use in railroad work, defines the degree of curve as the central angle subtended by a chord of 100 ft (30.48 m) in length; the second, used in highway work, defines the degree of curve as the central angle subtended by an arc of 100 ft (30.48 m) in length.

The terms and symbols generally used in reference to circular curves are listed next and shown in Figs. 11.1 and 11.2.

Figure 11.1: Circular curve.

Figure 11.2: Offsets to circular curve.

 PC = point of curvature, beginning of curvePI = point of intersection of tangentsPT = point of tangency, end of curve<i class="emphasis"> R</i> = radius of curve, ft (m)<i class="emphasis"> D</i> = degree of curve (see previous text)<i class="emphasis"> I</i> = deflection angle between tangents at PI, also central angle of curve<i class="emphasis"> T</i> = tangent distance, distance from PI to PC or PT, ft (m)<i class="emphasis"> L</i> = length of curve from PC to PT measured on 100-ft (30.48-m) chord for chord definition,on arc for arc definition, ft (m)<i class="emphasis"> C</i> = length of long chord from PC to PT, ft (m)<i class="emphasis"> E</i> = external distance, distance from PI to midpoint of curve, ft (m)

<i class="emphasis"> M</i> = midordinate, distance...