The ideal form of curve for the summit curve is a parabola.

The summit curve is a type of curve in transportation engineering that is used to transition between different gradients on a roadway. It is typically used when there is a change in the vertical alignment of the road, such as when going over a hill or a crest.

A parabolic curve is the ideal form for a summit curve due to its mathematical properties and its ability to provide a smooth transition between different gradients. Here are the reasons why a parabolic curve is considered the ideal form for a summit curve:

1. Constant rate of change:
A parabola has a constant rate of change, meaning that the slope of the curve is continuously changing at a constant rate. This allows for a smooth transition between different gradients, ensuring a comfortable and safe driving experience for motorists.

2. Minimal lateral acceleration:
A parabolic curve minimizes lateral acceleration, which is the force that pushes a vehicle sideways during a curve. By providing a smooth and gradual change in curvature, a parabolic curve reduces the lateral forces acting on a vehicle, resulting in a more comfortable and stable ride.

3. Balanced superelevation:
Superelevation, also known as banking, is the process of tilting the roadway towards the inside of a curve to counteract the centrifugal force experienced by vehicles. A parabolic curve allows for a balanced superelevation, ensuring that the bank angle is appropriate for the design speed of the curve.

4. Ease of construction:
Parabolic curves are relatively simple to design and construct. The mathematical properties of a parabola allow for precise calculations and measurements, making it easier for engineers to design and lay out the curve. Additionally, construction techniques such as stakeout and grading are well-suited to parabolic curves.

5. Aesthetically pleasing:
Parabolic curves are aesthetically pleasing and visually appealing. The smooth and symmetrical shape of a parabola is often considered more visually appealing than other curve forms, such as spirals or lemniscates.

In conclusion, a parabolic curve is considered the ideal form for a summit curve due to its constant rate of change, minimal lateral acceleration, balanced superelevation, ease of construction, and aesthetic appeal. Using a parabolic curve helps ensure a smooth and safe transition between different gradients on a roadway.