horizontal curve and its components

Horizontal curve play a pivotal role in shaping road and railway layouts, seamlessly transitioning between straight and curved segments. This design element ensures a smooth and safe journey for travelers.

Components of Horizontal Curves

Radius (R)

The radius defines the distance from the curve’s center to the centerline of the road or track. It plays a pivotal role in determining the curve’s flatness or sharpness.

Superelevation (or Banking)

Superelevation involves tilting the road or track along the curve to counteract centrifugal forces on vehicles. This banking effect raises the outer edge, providing a safer and more comfortable passage around the curve.

Length (Lc)

The length is the distance along the centerline from the curve’s inception to its termination. It gives a clear indication of the curve’s overall span.

Degree of Curve (D)

Measured in degrees, the degree of curve signifies the sharpness of the curve. It’s determined by the central angle formed by intersecting radii at the curve’s center.

Tangent (T)

The tangent is a straight section that connects two horizontal curves. It provides a seamless transition from straight paths to curved ones and vice versa.

Chord (C)

The chord is a straight line connecting the curve’s endpoints. It offers the shortest distance between two points on the curve.

External Distance (E)

E represents the distance from the curve’s center to the outer edge of the roadway or track. It’s crucial for understanding the road’s layout.

Internal Distance (I)

I is the distance from the curve’s center to the inner edge of the roadway or track. It helps assess available space within the curve.

Lateral Friction

This factor addresses the resistance provided by the road or track surface against a vehicle’s lateral movement. It’s instrumental in ensuring safe curve negotiation.

Sight Distance

Sight distance refers to the range a driver can clearly see ahead on a road. On a horizontal curve, this becomes vital for allowing drivers sufficient time to react to changing road conditions.

Transition Curves

These curves are integrated at the beginning and end of a horizontal curve. They facilitate a seamless transition between straight and curved trajectories.

Clear Zone

The clear zone encompasses the area beyond the road’s edge, providing a safe buffer for errant vehicles.

horizontal curve

Common Formulaes Used in Horizontal Curve

Mid – ordinate = R(1-cos(Φ/2))

External Distance = R(sec(Φ/2)-1)

Chord Length = 2Rsin(Φ/2)

Tangent Length = Rtan(Φ/2)

Curve Length (Lc) = R*Φ *(π/180)

Example 1 :-

The Radius (R) of horizontal curve is 80cm and deflection angle (Φ) = 114°, find the other componets?

solution :-

Mid – ordinate = R(1-cos(Φ/2))

= 80(1-cos(114/2)) = 36.428cm

External Distance = R(sec(Φ/2)-1)

= 80(sec(114/2)-1) = 66.886cm

Chord Length = 2Rsin(Φ/2)

= (2*80)*sin(114/2) = 134.187cm

Tangent Length = Rtan(Φ/2)

= 80tan(114/2) = 123.189cm

Curve Length (Lc) = R*Φ *(π/180)

= 80*114*(π/180) = 159.174cm


values may vary to some decimal places as it is angular calculation not linear calculation

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