Transition Curves in Railway Design

Transition curves are used in railway design to provide a gradual change in curvature between straight track and curved track sections. These curves help to reduce the abruptness of the change in direction and improve the comfort and safety of train operations. There are several types of transition curves used in railway design, each with its own characteristics and advantages. The correct answer is option 'A', Square Parabola, as it is not a type of transition curve used in railway design.

Explanation:

Square Parabola:
- The term "Square Parabola" is not a recognized type of transition curve used in railway design.
- It does not have a defined mathematical equation or geometric properties.
- Therefore, it is not a valid option for a type of transition curve used in railway curve design.

Cubic Parabola:
- The cubic parabola, also known as the cubic spiral, is a type of transition curve commonly used in railway design.
- It has a mathematical equation that represents a smooth and gradual change in curvature.
- The cubic parabola is defined by a third-degree polynomial equation and is widely used in railway alignments.

Euler's Spiral:
- Euler's spiral, also known as the clothoid or Cornu spiral, is another type of transition curve used in railway design.
- It has a mathematical equation that represents a gradual and continuous change in curvature.
- Euler's spiral is defined by Fresnel's integrals and is often used in high-speed railway alignments due to its smooth properties.

Bernoulli's Lemniscate:
- Bernoulli's lemniscate is a mathematical curve with a figure-eight shape.
- It is not typically used as a transition curve in railway design.
- While it can be used to represent a smooth change in curvature, it is not commonly employed in railway alignments.

In summary, the correct answer is option 'A', Square Parabola, as it is not a recognized type of transition curve used in railway design. The other options, cubic parabola, Euler's spiral, and Bernoulli's lemniscate, are all valid types of transition curves used in railway curve design.