- APSEd

# Length of a Summit Curve based on Sight Distance Criteria

Summit curve is a type of vertical curve having an upward gradient. The length of a summit curve is calculated based on only one criterion i.e., sight distance criteria.

## Summit Curve Concept

A summit curve is a type of vertical curve with an upward gradient i.e., convexity in an upward direction.

#### Where is a Summit Cuve Located?

It is used to join two gradients that fall under the following types.

Ascending and descending

Ascending and ascending

Ascending and horizontal

If you notice you will find that the summit curve is not used when a descending gradient meets an ascending gradient. The curve used in such a situation is called a valley curve. We had already covered valley curves in the length of the valley curve blog.

#### The Shape of a Summit Curve

The summit curve is provided in the shape of a simple parabola. It is chosen because it has a constant slope.

## Design Criteria of Summit Curve

Summit curves are designed based on a single criterion. This criterion is nothing but the sight distance required at each section of the highway.

If you recall from the valley curve design criteria there were two, i.e., sight distance and comfort criteria. But why is the comfort criterion not used here?

#### Reason for not using the Comfort Criterion in Summit Curve Design

Let us assume a fast-moving vehicle traversing from ascending to horizontal gradient over a summit curve. As the convexity is upward, the centrifugal force acts in the upward direction i.e., against gravity. Due to this upward centrifugal force, no pressure is exerted on the suspension system of the vehicle and therefore causes no discomfort for the passengers within. This is the reason why comfort is not considered a criterion in summit curve design.

## Summit Curve Formula

The length of a summit curve depends on the following parameters.

Deviation angle,

*N = |(±n1) - (±n2)|*Stopping sight distance (SSD)

Height of an obstacle from the road surface (h) ( i.e., 15 cm as per IRC)

Height of the eye level of the driver from the road surface (H) (i.e., 1.2m as per IRC)

There are four cases using which the length of the summit curve is found as discussed below.

#### Case 1: Lenght of Summit Curve > SSD

L = (N(S^2)) / (2((h^0.5)+(H^0.5))^2)

Substituting h = 0.15m and H = 1.2m we get,

*L = (NS^2) / 4.4*

where,

N = |(±n1) - (±n2)|

S - Stopping sight distance

#### Case 2: Lenght of Summit Curve < SSD

L = 2S - (2((h^0.5)+(H^0.5))^2)/N

Substituting h = 0.15m and H = 1.2m we get,

*L = 2S - (4.4 / N)*

where,

N = |(±n1) - (±n2)|

S - Stopping sight distance

#### Case 3: Lenght of Summit Curve > OSD

L = (N(S^2)) / (2((H^0.5)+(H^0.5))^2)

Substituting H = 1.2m we get,

*L = (NS^2) / 9.6*

where,

N = |(±n1) - (±n2)|

S - Stopping sight distance

#### Case 4: Lenght of Summit Curve < OSD

L = 2S - (2((H^0.5)+(H^0.5))^2)/N

Substituting h = 0.15m and H = 1.2m we get,

*L = 2S - (9.6/ N)*

where,

N = |(±n1) - (±n2)|

S - Stopping sight distance

For a better representation of the formulas please refer to the image below.

## Practise Problem

With this, we hope we had covered all the important topics related to the summit curve. Want us to cover a topic of your interest in a simple manner? Let us know in the comments below.