Calculating Transition Curve Length in Highway Design

The length of a transition curve on a highway is crucial for gradually introducing superelevation and curvature, ensuring a smooth and safe ride for vehicles transitioning from a tangent section to a circular curve.

There are several criteria used to determine the minimum length of a transition curve, including:

• Rate of change of centrifugal acceleration
• Rate of introduction of superelevation
• IRC empirical formulas (minimum length requirements)

In this problem, we are given the rate of introduction of superelevation, which allows us to calculate the length based on this specific criterion.

Given parameters:

• Design speed, $V = 100$ kmph
• Radius of horizontal curve, $R = 150$ m
• Carriageway width, $W = 7.5$ m
• Rate of superelevation, $e = 0.05$
• Rate of introduction of superelevation, $N = 1$ in 150
• Rotation is at the inner edge of the pavement.

We need to find the length of the transition curve, $L_s$.

The total amount of superelevation to be provided across the width of the carriageway is given by:

Total superelevation ($E$) = $e \times W$

Substituting the given values:

$\qquad E = 0.05 \times 7.5$ m

$\qquad E = 0.375$ m

The rate of introduction of superelevation is given as 1 in 150. This means that for every 150 units of horizontal length along the transition curve, the superelevation rises by 1 unit relative to the axis of rotation (in this case, the inner edge). To achieve a total superelevation rise of $E$, the required length of the transition curve ($L_s$) is calculated as follows:

Length of transition curve ($L_s$) based on superelevation rate = Total superelevation $\times$ Rate of introduction

$\qquad L_s = E \times N_{horizontal}$

Here, $N = 1$ in 150 means the slope is $1/150$. The horizontal length required to achieve a rise of $E$ is $E / (1/150) = E \times 150$.

$\qquad L_s = 0.375 \times 150$

Let's perform the calculation:

$\qquad L_s = 56.25$ m

This calculated length is based on the provided rate of introduction of superelevation. In design practice, this length would typically be compared with lengths derived from other criteria (like rate of change of centrifugal acceleration) and the maximum of these values, along with IRC minimum lengths, would be adopted as the final design length. However, based on the specific parameter provided (rate of introduction of superelevation) and the options available, the length calculated using this criterion is the intended answer.

Thus, the length of the transition curve is 56.25 m.