A road is provided with a horizontal circular curve having deflection angle of 55° and centre line radius of 250 m. A transition curve is to be provided at each end of the circular curve of such a length that the rate of gain of radial acceleration is $0.3 m / s^{3}$ at a speed of 50 km/h. Length of the transition curve required at each of the ends is

2.57 m

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1666.67 m

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35.73 m

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33.33 m

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Solution

The correct option is C 35.73 m
Radius of circular curve = 250 m
Rate of gain of radial acceleration,
$c = 0.3 m / s^{3}$

Speed,
$v = 50 k m / h$
$= \frac{50 \times 5 m / s}{18} = 13.89 m / s$

Length of transition curve,
$l = \frac{v^{3}}{C R}$
$= \frac{{13.89}^{3}}{0.3 \times 250} = 35.73 m . . . . . (i)$

As per IRC
$L_{s} = 2.7 \frac{V^{2}}{R}$
[for plain and rolling terrain]

$\Rightarrow L_{s} = 2.7 \times \frac{50^{2}}{250}$
$= 27 m . . . . . (i i)$
Length of transition curve will be maximum of two
$∴ L_{s} = 35.73 m$

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