Degree of Curvature and Radius of Curvature

The sharpness or the smoothness of a curve depends on the degree of curvature, D, and radius of curvature, R, of the curve. 

The degree of curvature can be determined using the chord basis or arc basis.

The chord basis is defined as the central angle formed by a chord measuring 30.48 meters, as a general practice.

The radius of the curve can be calculated for any particular curve using the relation of chord basis.

As for the arc basis, the degree of curvature is determined as the central angle of a circle subtended by an arc measuring 30.48 meters. This method also helps find the radius of the curve in terms of the degree of curvature.

The radius of curvature is expressed as a multiple of 30.48 meters. A smaller radius indicates a sharper curve, while larger radii indicate gentler curves.

In railroad practice, long, gradual curves typically use the chord basis, where arc lengths are assumed to equal chord lengths. For highway curves and curved property boundaries, the arc basis is more commonly preferred.