Highway Engineering

Two formulae are required for the analysis of transition curves:

S=L^2 /24R (6.24)

L=V^3 /(3.6^3 ¥C¥R) (6.25)

where

Sis the shift (m)

Lis the length of the transition curve (m)

Ris the radius of the circular curve (m)

Vis the design speed (km/hr)

Cis the rate of change of radial acceleration (m/s^3 )

The value ofCshould be within the range 0.3 to 0.6. A value above 0.6 can

result in instability in the vehicle while values less than 0.3 will lead to exces-

sively long transition curves leading to general geometric difficulties. The design

process usually commences with an initial value of 0.3 being utilised, with this

value being increased gradually if necessary towards its upper ceiling.

The length of transition should normally be limited to (24R)0.5 (TD 9/93),

thus:

(6.26)

Shift

Figure 6.14 illustrates the situation where transition curves are introduced

between the tangents and a circular curve of radius R. Here, the circular curve

LRmax= 24

174 Highway Engineering

I Deflection angle q

T T¢

T 1 T 2

RR

Shift S

Transition curve Transition curve

Circular curve

B

q/ 2

Figure 6.14Tr ansition curves.