# Types of curves, Elements of Curve for Surveying in Civil Engineering

## Why Curve is Provided?

It is neither practicable nor feasible to have a straight highway or railway in a country. Their alignment requires some changes in direction due to the nature of terrain, culture, feature, or other unavoidable reason.

Such change in direction cannot be at sharp but have to be gradual which necessitates the introduction of curves in between the straights.

A regular curved path followed by a railway or highway alignment is called a curve.

The curve is provided to change the direction of the path as well as of the motion of the moving body smoothly. There are different types of curves. It may be circular, parabolic, or spiral.

## Types of curves

1. Horizontal Curve
2. Verticle Curve

## A) Horizontal Curve

Horizontal curve are used to change the alignment or direction of a road. They can be circular curves or circular arc. The main design criteria of a horizontal curve is the provision of an adequate safe stopping sight distance.

### The Types of horizontal curves are:-

1. Simple Curve
2. Compound Curve
3. Reverse Curve
4. Transition Curve

#### Simple Curve

The curve which is a single arc of a circle is known as simple curve or simple circular curve. It has same magnitude of radius throughout of curve.

It is tangential to both the straight lines AT1 and CT2 as shown in figure below.

#### Compound Curve

A curve which consist of two or more arcs of a different circle with different radii having different centers lying on the same side of the common tangent and which bends in the same direction is known as compound curve.

The center of the combined circle must lies in the same side of the circle to form compound curve.

#### Reverse Curve

A Curve that consists of two arcs of different circles of the same or different radii is known as a reverse curve.

The centers of two arcs are on the opposite sides of the curve and the two arcs turns in opposite directions with a common tangent at the junction of the two arcs.

#### Transition Curve

A curve of varying radius introduced between a straight and a circular curve is called a transition curve.

## Elements of Simple Circular Curve

1) Back Tangent:- The tangent T1I at T1 ( The point of commencement of curve) is called back tangent.

2) Forward Tangent:- The tangent IT2 at T2 (The endpoint of the curve) is called the forward tangent.

3) Point of intersection:- The point I where back tangent when produced forward and forward tangent backward meet is called point of intersection (PI).

4) Angle of intersection:- Angle between the back tangent T1I and forward tangent IT2 is called the angle of intersection of the curve.

5) Angle of Deflection:- The angle through which forward tangent deflects is called the angle of deflection of the curve. It may be either to the right or to the left. It is denoted by Delta (Shown in the figure in Triangular Shape).

6) Angle of commencement:- The point T1 where the curve originated from the back tangent is called point of commencement of the curve. It is also sometime called point of curve.

7) Point of tangency:- The point T2 where the curve joins the forward tangent is called tangency.

8) Tangent Distance:- The distance between the point of intersection (PI) and point of commencement of the curve or the point of intersection (PI) and point of tangency is called tangent distance or tangent length. It is denoted by T.

9) Length of the curve:- The total length of the curve from the point of commencement to the point of tangency is called the length of the curve. It is represented by (I).

10) Long Chord:- The chord joining the point of commencement and the point of tangency is called the long chord. It is denoted by L.

11) Mid Ordinate:- The ordinate joining the midpoint of the curve and long chord is called mid-ordinate.

12) Apex Distance:- The distance from the mid-point of the curve to the point of intersection (PI) is called apex distance or external distance. It is denoted by E.

## B) Vertical Curve

A vertical curve is used to join two intersecting grade lines of railway, highway or other routs to smooth out the change in vertical motion.

An abrupt change in the rate of grade would be either injurious or dangerous while a vehicle passing over it.

Thus, the verticle curve contributes to the safety, comfort and appearance.

A verticle curve may be either circular or parabolic. But a parabolic curve is preferred due to simplicity of calculating offset for setting out the verticle curve.

A parabolic curve provides the best riding qualities as the rate of change of slope of a parabola is constant.

The gradient or grade may be defined as a proportional rise or fall between two points along a straight line.

It is expresses either as a percentage (1%, 2%, 5% etc. or as a ratio (i.e 1 in 100, 1 in 200 etc).

The grades are classified into two categories:

These classification depends upon the direction of movement of vehicles.

Down grade:- If the elevation along the grade line decrease, it is said to be down grade or -ve grade. An upgrade becomes a downgrade if the direction of motion of the vehicles reversed.

### Types of Vertical Curve

1) Summit Curve

2) Valley or Sag Curve

Depending upon the different combinations of different grades, the following are different types of verticle curves.

1) An upgrade (+g1%) followed by a down grade (-g2%) i.e Summit Curve.

2) An Downgrade (-g1%) followed by an upgrade (+g2%) i.e Valley Curve.

3) An upgrade (+g1%) followed by another upgrade (+g2%) g2>g1 i.e Valley Curve.

4) An upgrade (+g1%) followed by another upgrade (+g2%) g1>g2 i.e Summit Curve.

5) A downgrade (-g1%) followed by another down grade (-g2%) g2>g1 i.e Summit Curve.

6) A Downgrade (-g1%) followed by another down grade (-g2%) g1>g2 i.e Valley Curve.

Happy Learning – Civil Concept

Contributed by,

Civil Engineer – Ranjeet Sahani