Length of Transition Curves

Hi, how've you been?

Length of Transition Curves:

Transition curves are provided in between a straight road and the Curve of a design radius. 

The radius of a transition curve varies from infinity to the design radius or vice verse.  The length of the transition curve must fulfill some requirements. It is designed to fulfill the following three conditions:

(a) Rate of change of centri-fugal Acceleration(C):

 C = (v^2/R)/t =  (v^2/R)/ (Ls/v) = v^3/( LsR)  m/sec^3

As per IRC recommendations, C= 80/(75+v)   m/sec^3

Here, C= allowable rate of change of centrifugal acceleration ( m/sec^3)

Ls= Length of the transition curve.

(b) Rate of introduction of Designed super-elevation:

If pavement is rotated about centre line,  then

1/N = (E/2)/Ls

=> Ls= EN/2 = e.B.N/2 = e.(W+We).N/2

If pavement is rotated about inner edge, then

I/N = E/Ls

=> Ls= EN = e.B.N= e.(W+We).N

 where, Ls= Length of transition curve

              B= width of the pavement

(c) By Empirical Formula given by IRC(Indian Roads congress):

It should not be less than
(i) For plain and ruling terrain:   Ls = 2.7 V^2/R

(ii) For mountainous and steep terrain: Ls = V^2/R

Find out the greatest length of the transition curve by the above three criteria and use to construct the transition curve.

thanks for kind visit!