# What is transition curve? Length of transition curve formula | Design

## What is transition curve?

A transition curve has a radius that decreases from infinity at the tangent point to a designed radius of the circular curve. It is provided on either side of the circular curve.

## Types of Transition curve

1) Spiral or Clothoid transition curve

2) Berneull’s Lemniscate transition curve

3) Cubic Parabola transition curve

## Design of Transition curve i.e length of transition curve formula

The design of the transition curve is done to find out the minimum length of transition curve for a given radius. The length of the curve is designed to fulfill three conditions.

• Rate of change of centrifugal acceleration to be developed gradually.
• Rate of the introduction of the designed super elevation is to be at a reasonable rate.
• Minimum length by IRC formula

Maximum lengths obtained from the above condition are adopted in any particular case.

#### 1) By rate of change of centrifugal accleration

Let, Length of transition curve be ( Ls )

Velocity of vehicle = v m/sec

time = t sec.

Then,

Where, ( Ls ) = v x t

Rate of change of centrifugal acceleration (C) = v2/R.t

The rate of change of centrifugal acceleration is selected in order to provide comfort to passengers. Comfort consideration in one country may be luxury in another country.

Hence, different recommendation exist from country and country varies from 0.3 m/sec3 to 1 m/sec3 . In Indian road design practices following recommendations are noted.

a) for speed upto 32 kmph, Cmax= 0.76 m/sec3

b) for speed exceeding 96 kmph, Cmax= 0.46 m/sec3

c) for speed between 32 kmph to 96 kmph, Cmax= 80/(75+v) m/sec3

#### 2) By rate of introduction of super elevation

The full value of superelevation has to be obtained within the length of the transition curve. hence the length of the transition curve should be sufficient enough to change the road surface cambered shape to a fully super-elevation surface without any distortions.

N= rate of introduction of superelevation.

Its value is,

1 in (120-150) – Plain terrain

1 in 100 – Built-up area

1 in 60 – Hilly area

From the figure, for small Triangle ABC,

#### 3) By Empirical Formula

1) For plane and rolling terrain

2) For mountain and steep terrain

The larger value of length is adopted among these three methods.

## Numerical Example of Transition Curve

Q) A two-lane highway in terrain has a curve of a radius of 70 m. The design speed is 43 km/hrs. Determine the length of the transition curve.

Solution:-

Calculation of length of transition curve,

1) By rate of change of centrifugal acceleration

2) By rate of introduction of super elevation

3) By empirical formula