Transition curve in surveying - Type, Definition, Requirements

Definition of Transition Curve can be given as following.

• The Transition Curve is a Horizontal Curve of Varying Radius which we can use to connect Straight line to Circular curve.

The radius of curve is varying from infinite to certain fix value.

Generally, we provide transition curve at both ends of the circular curve. 

Sometimes we also provide it at the end of compound curve. 

This is useful for Transportation engineer, Highway Engineering and in Surveying.

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Why transition curve needed?

Without such a curve there is a risk of overturning of train or truck. This vehicle can slip and there is risk of accidents on road. 

Transition curve provide gradual increase of curvature which help a driver to accelerate vehicle. It also permits vehicle to drive at higher speed in curve.

What is requirement for curve to be a transition curve?

There is some conditions that need to be satisfied. The basic requirements is as following.

• It's radius must be infinite at origin on the tangent.
• Where the circular curve meet at that curve, on that point radius must be equal to circular curve's radius.
• There must be not become any difference between rate of increase of super elevation and the rate of increase of curvature.

Different types of transition curve

There is some different types of curve that satisfies the condition of transition curve.

The following are main types:

• Ideal curve or Cubic spiral
• Cubic parabola
• Lamiscate curve

These are main types which satisfied the requirements for transition curve.

Which curve is best for railway?

The Cubic parabolic and ideal curve is most effective for railway and train purpose when turning is very effective by using Cubic parabolic or Cubical spiral.

Which curve used for Highway?

For the Highway, There is need of Curvature for both Heavy and Light Weight Vehicles. For this Leminscate curve is best in which the radius is relate with sine function.

What is Cubic spiral curve?

The Cubicle spiral curve is very important curve.

It is one type of transition curve which have property in it's equation such as it follow Cubic rule of curve.

It has following mathematical characteristics:

• It is type of a transition curve in which the perpendicular offset from tangent is proportional to cube of distance measured on the curve.

• The perpendicular offset from the straight line or tangent is inversely proportional to radius of circular curve.

• In the Cubic spiral curve, The offset is inversely proportional to total length of the transition curve.

If radius of circular curve is R, distance measured along curve is l, the total length of transition curve is L and the perpendicular offset from tangent is z then we can write the equation as below:

z = l³/6RL

From this equation, we can write Clothoid equation as

l³=6zRL

Cubic spiral curve also called Clothoid.

This is ideal shape of transition curve because it have property and it satisfies all criteria for it.

What is Cubic Parabola Curve?

Cubic Parabola Curve is one type of transition curve which satisfies following relationship:

z = x³/6RL

This Curve is different from Cubic Spiral Curve because it follows cube of x instead of cube of length upto that point.

From above relationship, we can write:

x³ = 6RLz

As we can see from equation, cube of x is proportional to R, L, and z, for any point on the curve.