Geomatics Engineering

Curves

Simple, transition and vertical curves — setting out the smooth horizontal and vertical alignment of roads and railways.

PART 1

Topic Breakdown & Traps

A horizontal curve connects two straights (tangents) through a circular arc of radius

R

and deflection angle

Δ

. Key elements are the tangent length

T = R tan (Δ/2)

and the curve length

L = \frac{π R Δ}{180}

. A transition curve introduces curvature gradually; its shift is

S = \frac{L _{t}^{2}}{24 R}

Tangent length:

T = R tan \frac{Δ}{2}

Length of circular curve:

L = \frac{π R Δ}{180}

Degree of curve (30 m arc):

R = \frac{1718.87}{D}

Shift of transition curve:

S = \frac{L _{t}^{2}}{24 R}

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**Tangent length uses $tan (Δ/2)$ **, not $tan Δ$ — half the deflection angle.
⚠
**Curve length needs $Δ$ in degrees** with the $π /180$ factor (or radians directly).
⚠
Two degree-of-curve definitions exist (arc vs chord) — GATE usually uses the 30 m arc definition.

PART 2

Q1BASIC1 Mark · NAT

A circular curve has

R = 300 m

and deflection angle

Δ = 60°

. Its tangent length is _____ m.

Q2MEDIUM2 Marks · NAT

For

R = 300 m

and

Δ = 60°

, the length of the circular curve is _____ m.

Q3HARD2 Marks · NAT

A transition curve of length

60 m

is introduced on a curve of radius

300 m

. The shift is _____ m.