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A vehicle negotiates a transition curve with uniform speed v. If the radius of the horizontal curve and the allowable jerk are R and J, respectively, the minimum length of the transition curve is
1. \(\frac{{{R^3}}}{{\left( {vJ} \right)}}\)
2. \(\frac{{{J^3}}}{{\left( {Rv} \right)}}\)
3. \(\frac{{{v^2R}}}{{\left( {J} \right)}}\)
4. \(\frac{{{v^3}}}{{\left( {RJ} \right)}}\)

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Correct Answer - Option 4 : \(\frac{{{v^3}}}{{\left( {RJ} \right)}}\)

Concept:

Transition curve is provided to change the horizontal alignment from straight to circular curve gradually and has a radius that decreases from infinity at the straight end (tangent point) to the desired radius of the circular curve at the other end (curve point).

The rate of change of centrifugal acceleration is called jerk. The length of the transition curve depends on three criteria

  1. Rate of change of centrifugal acceleration
  2. Rate of change of superelevation
  3. Empirical formula's

1. Rate of change of centrifugal acceleration:

\({{\rm{L}}_1} = \frac{{{{\rm{v}}^3}}}{{{\rm{CR}}}}\)

v - Design speed in m/sec;

R - Radius of the horizontal curve, C - Rate of change in centrifugal acceleration or jerk

IRC suggests that \({\rm{C}} = \frac{{80}}{{75 + 3.6{\rm{v}}}}\) [C ranges from 0.8 to 0.5]

Rate of change of super elevation:

\({{\rm{L}}_2} = {\rm{Be'N}}\)

 e’ - Effective superelevation, N - The rate of change in super-elevation  

B - Total width of pavement including the widening if any

When the pavement is rotated about center e = e/2

When the pavement is rotated about the inner edge e = e

IRC Empirical Formula:

\({{\rm{L}}_3} = \left\{ {\begin{array}{*{20}{c}} {\frac{{2.7{{\rm{V}}^2}}}{{\rm{R}}},\;\;For\;plain\;and\;rolling\;terrain}\\ {\frac{{{{\rm{V}}^2}}}{{\rm{R}}},\;\;For\;hilly\;and\;steep\;terrain} \end{array}} \right.\)  where V is the speed in km/hr and R is the radius of horizontal curve

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