Types and Design of Curves on Roads

As discussed in the Radius of Curvature blog, this article covers the fundamental principles of road curves in modern civil engineering.

1) Horizontal Curves

Horizontal curves are provided to change the direction of the road in a horizontal plane.

a) Simple Curves

A single arc of a circle connecting two straight tangents. It has a constant radius throughout.

b) Compound Curves

Consists of two or more simple curves of different radii turning in the same direction and joining at a common tangent point.

c) Broken-back Curves

Two simple curves in the same direction separated by a short straight section (tangent). These are generally avoided for aesthetic and safety reasons.

d) Reverse Curves

Two simple curves with opposite directions of curvature having a common tangent. These are used in hilly terrain but avoided on high-speed highways.

2) Vertical Curves

Vertical curves are provided to provide a smooth transition between two different gradients.

• Summit Curves: Convex upwards (e.g., reaching a hilltop).
• Sag (Valley) Curves: Concave upwards (e.g., reaching the bottom of a hill).

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Design of Horizontal Curves (IRC Standards)

The fundamental equation for equilibrium on a curve is:

\[ e + f = \frac{V^2}{127R} \]

Where:

• \(e\) = Rate of superelevation
• \(f\) = Coefficient of lateral friction (IRC suggests 0.15)
• \(V\) = Design speed (km/h)
• \(R\) = Radius of the curve (m)

Example 2: Superelevation Rate Calculation
Given: \(V = 60\) km/h, \(R = 300\) m, \(f = 0.15\)
For mixed traffic, IRC recommends: \[ e = \frac{(0.75V)^2}{gR} \approx \frac{V^2}{225R} \] \[ e = \frac{60^2}{225 \times 300} = \frac{3600}{67500} \approx 0.053 \ (5.3\%) \] Since \(0.053 < 0.07\) (max limit), we provide 5.3% superelevation.

Example 3: Minimum Ruling Radius
Given: \(V = 80\) km/h, \(e_{max} = 0.07\), \(f = 0.15\)
\[ R_{min} = \frac{V^2}{127(e + f)} = \frac{80^2}{127(0.07 + 0.15)} \approx 229 \text{ m} \]

Sight Distance Reference

Design Speed (km/h)	SSD (Stopping Sight Distance)	ISD (Intermediate Sight Distance)	OSD (Overtaking Sight Distance)
100	180 m	360 m	640 m
80	120 m	240 m	470 m
60	80 m	160 m	320 m

Note: Always refer to the latest IRC:73 for geometric design standards in India.