As per IRC, the minimum length of transition curve for a mountainous terrain road with radius of curvature 100 m and design speed of vehicle 100 kmph is

Concept: 

Length of transition curve 

Based on IRC Formula

\({l_s} = \frac{{{V^2}}}{R}\) for Hilly terrain and \({l_s} = \frac{{2.7{V^2}}}{R}\) for Plain and Rolling terrain.

Where

Ls = length of the transition curve (m),  V = speed of the vehicle (km/hour),

 R = radius of the transition (m),

Calculation:

Given,

Design Speed = 100 kmph, Radius (R) = 100 m

iii) By empirical formula

For Mountainous or Hilly Terrain 

\({\rm{V}} = \frac{{{{\rm{V}}^2}}}{{\rm{R}}} = \frac{{ {{100}^2}}}{{100}} = 100{\rm{\;m}}\)

∴ The length of the transition curve-based IRC empirical formula is 100 m

Additional InformationLength of transition curve (Maximum value is to be considered among the below options)

a) Based on the rate of change of centrifugal acceleration (c)

\({{\rm{l}}_{\rm{s}}} = \frac{{{v^3}}}{{c \times R}}\)

where \(c = \frac{{80}}{{75 + V}}\) ……….. c value should be between 0.5 to 0.8

b) Based on the rate of change of superelevation (e)

1. Superelevation attained by rotation about the inner edge or outer edge

\({l_s} = eN\left( {w + w \times e} \right)\)

2. Superelevation attained by rotation about the center

\({l_s} = \frac{{eN\left( {w + w \times e} \right)}}{2}\)

c) Based on IRC Formula

\({l_s} = \frac{{{V^2}}}{R}\) for Hilly terrain and \({l_s} = \frac{{2.7{V^2}}}{R}\) for Plain and Rolling terrain.

Where

Ls = length of the transition curve (m), v = speed of the vehicle (m/s), V = speed of the vehicle (km/hour),

e = required superelevation, N = rate of change of superelevation to be attained, R = radius of the transition (m), and

w = width of road/pavement