# Transition Curves in Highway Engineering | Set Back Distance5 min read

## What Is Transition Curves in Highway:

When a vehicle traveling on a straight road enters into a horizontal curve instantaneously, it will cause
Discomfort to the driver. To avoid this, it is required to provide a transition curve. This may be provided either
between a tangent and a circular curve or between two branches of a compound or reverse curve.

The objectives of providing a transition curve are:
(i) To gradually introduce the centrifugal force between a straight and circular curve
(ii) To avoid a certain jerk.
(iii) To the gradual introduction of superelevation and extra widening.
(iv) To enable the driver to turn the steering gradually for comfort and security
(v) To improve aesthetic appearance.

A Transition curve should satisfy the following conditions:

(i) It should meet the straight path tangentially.
(ii) It should meet the circular curve tangentially.
(iii) It should have the same radius as that of the circular curve at its junction with the circular curve.
(iv) The rate of increase of curvature and superelevation should be the same.

The length of transition curve required on a horizontal highway curve depends upon the following
Factors:
(i) Radius of the circular curve. R
(ii) Design speed, V
(iii) Allowable rate of change of centrifugal acceleration, C
(iv) Maximum amount of super elevation which depends on the maximum rate of superelevation.
and the total width of the pavement, B at the horizontal curve.
(v) Allowable rate of introduction of superelevation.
(vi) Rotation of pavement cross-section either about the inner edge or the centre line.

### Different Types of Transition Curves:

The types of transition curves commonly adopted in horizontal alignment of highways are:
(i) Spiral or Clothold
(ii) Bernoulli’s Lemniscale
(iii) Cubic Parabola

The general shapes of these three curves are shown in Figure. All the three curves follow almost the same path upto deflection angle of 40, and practically there is no significant difference even up to 9º. In all these curves, the radius decreases as the length increases.

### Length of Transition Curve:

The length of the transition curve is designed to fulfill three conditions i.e.,
(i) rate of change of centrifugal acceleration to be developed gradually
(ii) rate of introduction of the designed superelevation to be at a reasonable rate, and
(iii) minimum length by IRC empirical formula

The length of the transition curve fulfilling all the three conditions (or the highest of the three values) is
generally accepted.

Length of Transition Curve by the Rate of Change of Radial Acceleration

$\huge Ls\ =\ \frac{V^3}{CR}\ =\ \frac{0.0215V^3}{CR}$

where V = Velocity of the vehicle in kmph
R=Radius of the curve in m

The rate of change of centrifugal acceleration is given by an empirical formula recommended by IRC

$\huge C\ =\ \frac{80}{75+V}$[V= velocity in kmph]

Subject to a maximum of 0.8 and minimum of 0.5.

Length of Transition Curve by an Arbitrary Rate of Change of Superelevation

The length of the transition curve can be such that tho superelevation (e) is applied at a uniform rate of 1 in N. The length of transition curve ‘Ls’ given by

(i) When pavement is rotated about the inner edge

L = eN(W+We)

where,  1/N = Rate of change of superelevation
N = 150 ( Plain and Rolling terrain)
N = 60 (Hilly Area)
W = Width of pavement
We = Extra widening

(ii) When pavement is rotated about the center

$\huge Ls\ =\ \frac{eN\left(W+We\right)}{2}$

Empirical Formula for the Length of Transition Curve Recommended by IRC

For plain and rolling terrain,

$\huge Ls\ =\ 2.7\ \frac{V^2}{R\ }\ m$

For mountainous and steep terrain,

Ls = V²/R m

### Design Steps of Horizontal Transition Curve Length:

The design steps for the transition curve in horizontal alignment are given below:

(i) Find the length of the transition curve based on the allowable rate of change of the radial acceleration
(i) Find the length of the transition curve based on the allowable rate of change of superelevation
(ii) Determine the minimum required value of ‘Ls’ as per the empirical formula
(iv) Adopt the highest value of ‘Ls’ given by (i), (ii), and (iii) above as the design length of the transition curve

## Setting out of Transition Curve:

When a transition curve is introduced between a straight and circular curve, then a circular curve has to be shifted so that the transition curve meets the circular curve tangentially.

The shift (S) of a circular curve is given by

$\huge S\ =\ \frac{Ls^2}{24R}$

(Ls = Length of transition curve)

## Set Back Distance:

Set back distance is the clear distance required from centre line of the curve to the obstruction on the
the inner side of the curve to provide adequate sight distances as shown in Figure

There are two cases in the calculation of setback distance:

Case-1: When the length of a horizontal curve is greater than the sight distance (Lc > SD)

(a) For Single Lane:
Let. M is the setback distance and sight distance (SD) is measured along the center line, then the
the setback distance from the centerline of the road is given by

$\huge M\ =\ \left(R-R\cos\ \frac{\alpha}{2}\right)\ m$As ‘∝’ is in degree so,  $\huge \frac{\alpha}{2}\ =\ \frac{SD}{2R}\cdot\frac{180\degree}{\pi}$

(b) For Multi Lane:
Let 2d is the total width of a lane, then setback distance from the center line of the road having only two-lane is given as

$\huge M\ =\ R-\left(R-d\right)\cos\ \frac{\alpha}{2}\$

Similarly, for a road of ‘n’ lanes, setback distance is given by

$\huge M\ =\ R-\left(R-\left(n-1\right)d\right)\cos\ \frac{\alpha}{2}\$

Case-2: When the length of a horizontal curve is less than the sight distance (Ls < SD).

(a) For Single Lane:
Hence, the setback distance from the centre line of the road is

$\huge M\ =\ \left(R-R\cos\ \frac{\alpha}{2}\right)\ +\ \left(\frac{S-Lc}{2}\right)\ \sin\frac{\alpha}{2}\$

and

$\huge \frac{\alpha}{2}\ =\ \frac{Lc}{2R}\cdot\frac{180\degree}{\pi}$

(b) For Two-Lane:
The setback distance from the centre line of the road

$\huge M=R-\left(R-d\right)\cos\frac{\alpha}{2}+\left(\frac{S-Lc}{2}\right)\ \sin\frac{\alpha}{2}$

And

$\huge \frac{\alpha}{2}\ =\ \frac{Lc}{2\left(R-d\right)}\cdot\frac{180\degree}{\pi}$The setback distance from centre line of the inner lane is

$\huge M=\left(R-d\right)-\left(R-d\right)\cos\frac{\alpha}{2}+\left(\frac{S-Lc}{2}\right)\ \sin\frac{\alpha}{2}$

And

$\huge \frac{\alpha}{2}\ =\ \frac{Lc}{2\left(R-d\right)}\cdot\frac{180\degree}{\pi}$