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Types Of Curves In Surveying Work

Types Of Curves In Surveying Work.

What Is The Curve?

The Curves are generally the horizontal &/or vertical bends that are usually used on highways & the railways when it is necessary to change the alignment of the route. when 2 points are located at the different levels, it becomes necessary to give the curve.

This curve usually helps to connect the points lying at the different levels in such a way that the vehicles moving on that route could move with ease, safety & comfort. A proper alignment or the curve can provide smoother movement of the vehicles from 1 point to another, located at the different levels.


A curve is introduced at the intersection of 2 straights to effect the gradual change in the direction. This change in direction may be in the horizontal plane or a vertical plane. So curve is provided to the route according to its direction, i.e. either in the vertical plane or in a horizontal plane, respectively.

Types Of Curves In Surveying Work

Curves in the surveying are classified into 2 main types. They are as follows.

  1. Horizontal curves.
  2. Vertical curves.

1 – Horizontal Curves.

The horizontal curve is provided where 2 straight lines intersect with each other in the horizontal plane. When a curve is given in the horizontal plane, it is known as a horizontal curve. A horizontal curves are further divided as follows:

  1. Simple curve.
  2. Compound curve.
  3. Reverse curve.
  4. Transition curve.
  5. Combined curve.

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a) – Simple Curve.

The simple curve is a single arc of the circle, which is tangential to both the straight lines of route. There are a few elements of the simple circular curve discussed below.

Circular Curve

Back Tangent.

The line of the tangent before the beginning of the curve is known as a back tangent.

Forward Tangent.

The tangent line after finishing of the curve is known as the forward tangent.

Point Of the Intersection.

The point where the back tangent & the forward tangent intersects, is known as the point of intersection.

Intersection Angle.

The angle between the back & the forward tangent is known as intersection angle.

Angle Of Deflection.

An the angle through which the forward tangent deflects is known as angle of deflection.

Point of curvature.

The point at the beginning of the curve, where the alignment changes the tangent into the curve, is known as point of the curvature.

Point Of Tangency. 

The point at the end of the curve, where the curve changes into the tangent, is known as point of the tangency.

Tangent distance.

The distance between the point of the curvature & point of intersection is known as the tangent distance.

Length Of Curve.

The total length of curve from the point of curvature to the point of intersection is known as the length of curve.

Long Chord. 

The chord joining the point of curvature & the point of tangency, is known as the long chord.

Normal Chord.

The chord between 2 successive pegs on the curve, is known as a normal chord.


The chord shorter than the normal chord is known as a sub-chord.


The distance between the midpoint of the curve & the midpoint of the long chord, is known as mid-ordinate.

External Distance.

The distance between the point of intersection & the midpoint of the curve, is the external distance.

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b) – Compound Curve.

The compound curve comprises 2 or more circular arcs of the different radii with their centers of the curvature on the same side of the common tangent. It is where the cutting & filling of soil is to be avoided. Compound curves are necessary whenever the space restrictions rule out the signal circular curve & when there are property boundaries.

Compound Curve

c) – Reverse Curve.

The curve consisting of 2 circular arcs of similar or different sizes radii having their centers on opposite sides of the common tangent at the point of reverse curvature is known as a reverse curves reverse curve is also known as the serpentine curve or S-curve due to its shape. The Reverse curves are used to connect 2 parallel roads or railway lines. It is generally used when 2 lines intersect at a very small angle.

Reverse Curve

The Reverse curves are best suited for hilly terrains & the highways used for relatively low-speed vehicles. Reverse curves are not advisable to use on the highways & railways which are meant for high-speed traffic movement because of the following reasons.

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1) – The sudden change in direction can be dangerous for the vehicles.

2) – The sudden change in the curvature & direction reduces the life of vehicles & also provides discomfort to the people traveling on that route.

3) – If the driver is the careless, it may cause the vehicle to overturn over the reverse curve.

d) – Transition Curve.

It is the curve of varying radius. The value of the radius of this type of the curve varies from infinity to a certain fixed value. It provides the gradual change from the straight line to the circular curve & again from the circular curve to the straight line. It is usually provided on both ends of the circular curve. The transition curves are provided on the roads & railways to lessen the discomfort at the sudden change in the curvature at the junction of a straight line & a curve.

Transition Curve

The transition curve has the following advantages.

1) – Transition curve reduces the probability of the overturning vehicles at the junction of the straight and the curve.

2) – It gives comfort to the passengers.

3) – It allows higher speeds for the vehicles at the curves.

4) – Transition curve reduces the wear & tear of the rail section, occurring due to unusual friction at the point of curve.

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v) – Combined Curve

The combination of the simple circular curve & the transition curve, is known as a combined curve. Combined curves are mostly preferred in the highways and railways.

When transition curves are provided at both ends of the circular curve, the curve formed is known as a combined or the complete curve.

Combined Curve

2) – Vertical curves.

The Vertical curves are usually provided when the highway or a railway crosses a ridge or a valley. The Vertical curves are provided when there is a difference of the level between 2 points. So to make the movement easy between these points, the vertical curve is provided. It makes the transition of the vehicle smooth & comfortable.

There are 2 main types of vertical curves.

  1. Summit curve, and
  2. Valley curve.

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a) – Summit Curve.

The vertical curve having its convexity in the upwards direction is known as the summit curve.

Summit Curve

The Summit curves are usually provided in the following cases.

1)  – When an upgrade is followed by the downgrade,

2) – When the steeper upgrade is followed by a milder upgrade, &

3) – When the milder downgrade is followed by a steeper upgrade.

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b) – Sag Curve Or Valley Curve.

The vertical curve having its convexity in the downwards direction or when it is the concave upwards is known as a valley curve. It is also known as sag curve.

Sag Curve Or Valley Curve

The sag curve or a valley curve is usually formed in the following cases.

1) – When the downgrade is followed by an upgrade,

2) – When the steeper downgrade is followed by a milder upgrade, &

3) – When the milder upgrade is followed by a steeper upgrade.

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About Raja Junaid Iqbal

Hi My name is Raja Junaid Iqbal and i am Land Surveyor by Profession but I've specialized in the field of Q,S and land development. As Professional Surveyor I engaged my self in all over the Gulf since 14 years.

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