Summit Curve:

A summit curve is defined as a curve that is used to connect two gradients, where one gradient is steeper than the other. It is used to ensure that the train can climb up the steep gradient without losing too much speed.

Ideal form of Summit curve:

The ideal form of the curve for the summit curve is a parabola. However, due to practical limitations, it is not possible to construct a parabolic curve. Hence, an approximation of the parabolic curve is used, which is known as a cubic parabola.

Reasons for parabolic curve being the ideal form of Summit curve:

1. Constant rate of change of centrifugal force:

A parabolic curve has a constant rate of change of centrifugal force. This ensures that the train can maintain a constant speed while negotiating the curve.

2. Uniform rate of curvature:

A parabolic curve has a uniform rate of curvature. This ensures that the train experiences the same amount of lateral acceleration throughout the curve.

3. Minimum length of curve:

A parabolic curve requires the minimum length of curve to connect two gradients. This ensures that the train can maintain its speed while negotiating the curve.

4. Easy to construct:

A parabolic curve is easy to construct and maintain. This reduces the construction and maintenance costs of the railway line.

Conclusion:

Hence, the ideal form of the curve for the summit curve is a parabola. However, due to practical limitations, an approximation of the parabolic curve is used, which is known as a cubic parabola.