Types Of Circular Curves In Surveying

Types Of Circular Curves In Surveying

What Are Curves

Curves are regular bends in communication lines such as roads, trains, and canals that cause a progressive change in direction. They are also employed in the vertical plane at all grade changes to avoid an abrupt change in slope at the apex.

Horizontal curves are those that are provided in the horizontal plane to have a progressive change in direction, whilst vertical curves are those that are offered in the vertical plane to have a gradual change in grade.

Curves are drawn on the ground along the work’s center line. They can be either circular or parabolic.

Why Is A Curve Provided?

A straight roadway or railway in a country is neither practicable nor possible. Because of the nature of the terrain, culture, feature, or other inescapable reason, their alignment necessitates occasional shifts in direction.

Such a shift in direction cannot be abrupt, but must be gradual, necessitating the inclusion of curves in between the straights.

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

The curve is used to gently shift the direction of the path as well as the velocity of the moving body. Curves come in a variety of shapes and sizes. It might be round, parabolic, or spiral in shape.

Types of curves

  • Horizontal Curve
  • Vertical curves

Horizontal Curve

Horizontal curves are used to adjust the alignment or direction of a route. They can be circular curves or circular arcs. The key design criterion for a horizontal curve is the supply of an acceptable safe stopping sight distance.

The Types of horizontal curves are;

  • Simple Curve
  • Compound Curve
  • Reverse Curve
  • Transition Curve
  • Broken Back Curve

Simple Curve

It’s a circular curve made out of a single arch with a consistent radius. It is commonly represented by a chord of 30 m. or by the length of the radius, which can be determined using the following equation.

R = 1746.5/D


  • R is the radius of the curve.
  • D is the curve’s degree.

Simple Circular Curve Elements

  • Back Tangent: The tangent T1I at T1 (the point where the curve begins) is referred to as the back tangent.
  • Forward Tangent: The forward tangent is the tangent IT2 at T2 (the curve’s terminal).
  • Point of intersection: The point I where the back tangent produced forward and the forward tangent produced backward meet is referred to as the point of junction (PI).
  • Angle of intersection: The angle formed by the rear tangent T1I and the forward tangent IT2 is known as the curve’s angle of junction.
  • Angle of Deflection: The angle through which the forward tangent deflects is referred to as the curve’s angle of deflection. It could be to the right or to the left. Delta represents it (Shown in the figure in Triangular Shape).
  • Angle of commencement: The point T1 where the curve began from the back tangent is referred to as the curve’s point of commencement. It is also known as the point of curvature.
  • Tangency: Tangency is the point T2 where the curve meets the forward tangent.
  • Tangent distance or tangent length is the distance between the point of intersection (PI) and the point of commencement of the curve or the point of intersection (PI) and the point of tangency. It is represented by the letter T.
  • Length of the curve: The length of the curve is the overall length of the curve from the point of commencement to the point of tangency. It is symbolized by (I).
  • Long Chord: The long chord is the chord that connects the points of commencement and tangency. It is represented by the letter L.
  • Mid Ordinate: The ordinate that connects the middle of the curve with the long chord is known as the mid-ordinate.
  • Apex Distance: The distance from the curve’s midpoint to the point of intersection (PI) is known as the apex distance or external distance. It is represented by the letter E.

Compound Curve

This is a curve made up of two or more basic curves of varying radius that turn in the same general direction. To avoid cutting or filling, this sort of curve is employed.

They become advantageous when a road must be placed to match a specific terrain, such as a layout between a river and a cliff, or when the curve must follow a specific direction.

Reverse curve

This curve is made up of two basic curves with the same or different radius that turn in the opposite direction.

These bends are appropriate for railways in mountainous areas and for crossings in station yards. The deviation curve is formed when a circular curve is made up of two reverse curves with or without a straight line in between.

This style of curve is commonly utilized in accident sites and for substantial track repair work on worn-out tracks. This maintains the railway going in the original direction after a required deviation.

Transition Curve

When a vehicle enters or exits a finite radius circular curve. It is subjected to an outward centrifugal force. This shocks both the passenger and the driver.

The major aim of the transition curve is to allow a vehicle traveling at high speeds to safely and comfortably transition from the tangent portion to the curves section, and then back to the tangent part of a railway.

The transition curve raises the outer rail over the inner rail, decreasing shocks and severe erk on the moving railway vehicle.

It reduces rail wear on curved rails and improves comfort to passengers due to the train’s smooth operation.

The most common type of transition curve:

Lemniscate curve –In this transition curve, the radius reduces as the length grows, resulting in a modest drop in the rate of gain of radial acceleration.

L = C✓sin2h

  • L = length of polar ray in meters
  • h = polar angle in radions
  • C = A constant

Spiral curve – This is an excellent transition curve. The radius of this curve is inversely proportional to the length travelled. As a result, the rate of change of acceleration in this curve is constant over its length.

Cubic parabolic curve – In the case of the curve, the rate of decrease of curvature is substantially lower for deflection angles.

4°to9°, but beyond 9°, the radius of curvature rapidly increases.

Y = X3/ (6RL)

  • Y = coordinate of any point
  • R = radius
  • L is the length of the curve.

Transition curve functions

They include:

  • A transition curve is typically used to connect a straight and a simple circular curve, or two simple circular curves.
  • These types of curves are typically supplied on both sides of circular bends to prevent super elevation and passenger discomfort.
  • To introduce a gentle transition from the tangent point to the circular curve and vice versa.
  • To progressively add the designed super elevation at the beginning of the curve.
  • To allow for the addition of further road expansion at the curve’s starting point.

Broken Back Curve

A broken back curve is formed by joining two circular curves of the same or different radius with a short common tangent. The center of the circular arcs is on the same side in broken back curves. Previously, these curves were used for railroad traffic. However, because this bend is not ideal for high-speed traffic, it is no longer used.

Vertical Curves

A vertical curve is an elevation curve that is presented during a change in slopes. Changes in slopes are required owing to a country’s terrain and to lessen the amount of earthwork.

Vertical curves can be circular or parabolic in shape. Because of the following, the parabolic shape is chosen.

  • Because of the flatness at the top of the parabolic shape, the seeing distance is increased. As a result, the likelihood of an accident is reduced.
  • Because of the consistent rate of change of grade, parabolic forms provide the best riding attributes.

Vertical curve types

  • Summit Curve
  • Valley Curve

Summit Curve

Summit curves are vertical curves with convexity pointing upwards. Summit curves are typically used when;

  • A position grade collides with a negative grade.
  • A position grade encounters a lighter position graded.
  • A position grade collides with a level stretch.
  • A Steelers bad grade meets a negative grade.

The centrifugal force generated by a vehicle moving along a summit curve acts in the opposite direction that its weight acts.

Valley curve

Vertical curves with downward convexity are known as sag curves. In most cases, sag curves are introduced when;

  • A negative grade collides with a positive grade.
  • A negative grade encounters a less severe negative grade.
  • A negative grade collides with a flat stretch.
  • A low grade meets a high rating for the Steelers.

The centrifugal force produced by a vehicle traveling over a valley curve acts in the same direction as the vehicle’s weight.


What is circular curve in surveying?

Curves are described as arcs with a finite radius that are given between intersecting straights to progressively negotiate a direction shift. This change in straight direction may occur in a horizontal or vertical plane, resulting in the production of a horizontal or vertical curve.

What is the different classification of curves?

Curves can be simple, compound, reversed, or spiraled. Compound and reverse curves are considered to be a composite of two or more simple curves, whereas the spiral curve is based on shifting radius.

How do you find the circular curve?

C = 2R sin (/2) can be used to compute the subchord. This equation is a subset of the long chord and total deflection angle equations. The following is the general case: Deflection angle C = 2R sin If the deflection angle of a subchord is known, it may be computed.

What are the types of vertical curve?

Vertical curves are classified into two types: sag curves and crest curves. Sag curves are used when there is a positive change in grade, such as valleys, while crest curves are used when there is a negative change in grade, such as hills.

How is a simple circular curve designated?

A curve can be defined by its radius or by the angle subtended at its center by a chord of a specific length. In India, a curve is defined by the angle (in degrees) subtended at its center by a chord of 30 meters (100 ft.) length. This angle is known as the curve’s degree (D).

What is a tangent curve in surveying?

Curve, tangent spiral point—The point at which straight alignment ceases and spiral alignment begins. Also known as T.S. curve, transition.

How many types of road construction curves are there?

In highway construction, there are two sorts of curves: horizontal curves and vertical curves. Curves are provided anytime a route changes direction from right to south (or vice versa) or its alignment changes from up to down (vice versa).

What is the difference between forward tangent and backward tangent?

The tangent line preceding the start of the curve is referred to as the Back tangent or the rear tangent. The Forward tangent is the tangent line that follows the end of the curve.

Is circle a curved line?

Curved lines create open and closed curves. A circle is a closed curve generated when a point moves in a plane at a constant distance from the center. Interesting fact. Geometry is a subject of mathematics that deals with various forms and solids composed of straight and curved lines.

What is the main difference between a circular curve and a spiral curve?

A spiral’s curvature must increase uniformly from beginning to conclusion. Its curvature is zero at the beginning, where it departs the tangent; at the end, where it joins the circle curve, it has the same degree of curvature as the circular curve it intercepts.

What is the name of curves?

By shape: astroid (star), deltoid (Greek letter Delta), cardioid (hear-shaped), conchoid of Nicomedes (mussel-shaped), nephroid (kidney-shaped), cycloid (circle, wheel), folia (leaf), Newton’s trident, serpentine (snake), Diocles’ cissoid (Ivy-shaped), rose

What is a horizontal curve?

Horizontal curves are those that alter the alignment or direction of the road (as opposed to vertical curves, which change the slope). A horizontal curve is involved in more than 25% of fatal crashes, and the vast majority of these crashes are caused by a deviation from the route.

What is the delta angle of a curve?

Delta is the angle formed by each curve from the center of a theoretical circle. Consider two straight line segments of length Radius that converge at the center of the circle and whose endpoints are at opposite ends of the arc curve.

The angle at which they converge will be delta.

How do you classify a curve?

By comparing the mean responses to the confidence intervals, curve shapes can be characterized as growing, decreasing, or unimodal 

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