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Q: Which of the following curves fulfils the requirements of an ideal transition curve in horizontal alignment of the highways, for such curves radius is inversely proportional to the length and centrifugal acceleration is uniform throughout the length?
  • A. Cubic parabolic curve
  • B. Circular curve
  • C. Spiral curve
  • D. Sine curve
Correct Answer: Option C - Spiral curve -The requirements of an ideal transition curve in horizontal alignment of the highways, for such curves radius is inversely proportional to the length and centrifugal acceleration is uniform throughout the length . Ideal shape of transition curve is clothoid which means "Euler spiral" whose curvature is equal to its arc length. Transition curve is a curve in plan which is provided to change the horizontal alignment from straight to circular curve gradually means the radius of transition curve varies between infinity to R or R to infinity. IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons: • It satisfies that rate of change of centrifugal acceleration is constant i.e., Ls × R = constant. Where Ls = length of transition curve R = radius of curve. • The calculation and field implementation of spiral curve is simple and easy. • It enhances aesthetics also.
C. Spiral curve -The requirements of an ideal transition curve in horizontal alignment of the highways, for such curves radius is inversely proportional to the length and centrifugal acceleration is uniform throughout the length . Ideal shape of transition curve is clothoid which means "Euler spiral" whose curvature is equal to its arc length. Transition curve is a curve in plan which is provided to change the horizontal alignment from straight to circular curve gradually means the radius of transition curve varies between infinity to R or R to infinity. IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons: • It satisfies that rate of change of centrifugal acceleration is constant i.e., Ls × R = constant. Where Ls = length of transition curve R = radius of curve. • The calculation and field implementation of spiral curve is simple and easy. • It enhances aesthetics also.

Explanations:

Spiral curve -The requirements of an ideal transition curve in horizontal alignment of the highways, for such curves radius is inversely proportional to the length and centrifugal acceleration is uniform throughout the length . Ideal shape of transition curve is clothoid which means "Euler spiral" whose curvature is equal to its arc length. Transition curve is a curve in plan which is provided to change the horizontal alignment from straight to circular curve gradually means the radius of transition curve varies between infinity to R or R to infinity. IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons: • It satisfies that rate of change of centrifugal acceleration is constant i.e., Ls × R = constant. Where Ls = length of transition curve R = radius of curve. • The calculation and field implementation of spiral curve is simple and easy. • It enhances aesthetics also.