The relation between the radius \((R)\) and degree \((D )\) of a curve is

Explanation:

The relation between the radius (R, in feet) and the degree of curve (D, in degrees) for a simple circular curve is given by the formula:

\(R=\frac{1719}{D}\)

• This is commonly used in railway and highway alignment design when the degree of curve is defined based on a chord length of 100 feet.
• The formula provides an easy way to convert between the degree of curve and the corresponding radius of curvature.

 Additional Information

Degree of Curve (D):

• The degree of curve is defined as the central angle subtended by a chord of fixed length, typically 100 feet in standard practice.

• It represents the sharpness of a curve — a larger degree of curve indicates a sharper curve, while a smaller degree indicates a flatter curve.

• It is used widely in geometric design of roads and railways for laying out curves in the field and in design drawings.

• The degree of curve provides a convenient way to express curvature without needing to specify the radius directly.

 Radius of Curve (R):

• The radius is the distance from the center of the circle to any point on the curve. It directly determines the curvature — a smaller radius means a sharper curve.

• Knowing the radius helps in calculating transition curves, vehicle dynamics, and super-elevation requirements for safe turning.

• In practice, curves with larger radii are preferred for higher-speed routes to reduce centrifugal force and increase comfort.