## What Are the Curves?

The gradual change of direction of regular bends is called curves. When the curves are provided in the horizontal plane, then itâ€™s called a horizontal curve.

When the curves are provided with some vertical elevation, then itâ€™s called a vertical curve. Curves mainly change the road slope and allow the vehicles to pass through it.

## Types of Curves in Surveying

Curves are the geometrical arc provided to gradient change or alignment change. These curves are mainly two types, those are-

- Horizontal Curve
- Vertical Curve

## What Are Horizontal Curves?

A horizontal curve is a type of curve that is provided to change the direction of the alignment. Normally, a flat curve is provided with the conjunction of the transition curve. It is mainly provided to access a particular locality.

## Types of Horizontal Curves

There are mainly seven types of horizontal curves are there. Those seven types of curves are

### 1. Simple Curve

The simple curve is a type of curve that is created by single radios. This type of curve is mainly effective for large radios and for slow-moving vehicle. In term of the degree of the curve, this curve is expressed.

In this type of curve, the radius is calculated by the following formula-

R = 1647.5/D

Where,

R= radius of the curve

D= degree of curve

### 2. Compound Curve

A compound curve is a type of curve where two or more different radius curve is joined together to form a single curve. This type of curve is mainly constructed to avoid the cutting filling option.

When the road layout is aligned between a river and a cliff, then this type of curve is highly effective to design.

### 3. Reverse Curve

This type of curve is contained with two simple types of curve with different radius in the opposite direction. This is suitable for station yards crossing and hilly regions.

We know, when a circular curve consists of two reverse curves with or without a straight line is known as a deviation curve. This is mainly used in accident places and major repair work on worn-out tracks.

**4. Transition Curve**

A transition curve is a curve where a vehicle enters or leaves from the curve with a finite radius. This is the main cause of configuring a centrifugal force.

The main purpose of this curve is to allow the vehicles to maintain a proper speed in a safe and comfortable fashion. In railway tracks, a super elevation is provided to the outer track for maintaining a proper speed with safety.

### 5. Lemniscate Curve

In this type of curve, radius decreases and length increases.

In the following equation, we can find out radial acceleration-

**L = Câˆšsin ^{3}h**

L= length of polar ray in meter

h= polar angle in radius

C= constant

### 6. Spiral Curve

The curve length of this type of curve is proportional to the traverse length. This type of curve is an ideal transition curve. In this curve, the rate of change of acceleration is uniform.

### 7. Cubic Parabolic Curve

In this type of curve, the rate of curvature is higher than the deflection angle.

Here, by the equation-

**Y = x ^{3} /6RL**

Y= Coordinate of a point

R= Radius

L= Length of the curve

## What Are Vertical Curves?

Vertical curves are the types of curves where a super elevation is provided for the change of gradient. Different types of topographical conditions are found in different country thatâ€™s the main cause of gradient change. We also provide a vertical curve to reduce the earthwork process.

## Types of Vertical Curves

There are mainly two types of vertical curves are observed, those are

- Summit Curve.
- Valley Curve.

### 1. Summit Curve

Summit curves are that type of curve that have their convexity upward. In this summit curve, the centrifugal force is acted upward against gravity.

For this action, the passengers do not feel discomfort. When we design the summit curve, then we design overtaking sight distance and stopping sight distance separately.

### 2. Valley Curve

Valley curves are that type of curve where the convexity is downward; sometimes, it also called the sag curve.

In the valley curve, the centrifugal force is acted downwards, so there is another addition of self-weight in the vehicle. To design a valley curve, an allowable rate change of centrifugal force is added.

## Application of Curves

**Application of Horizontal Curve:**The most important element of road geometry is a horizontal curve; the main function of a horizontal curve is to provide the smooth transition curve; thatâ€™s why it is widely used in highway curves. So, it is the application of horizontal curve.**Application of Vertical Curve:**It is also a very important curve in road geometry. The vertical curve is mainly used where the gradient of the road is changed, so it is widely used in a mountain region. Another application of the vertical curve is the Hairpin bend the curve.

**FAQ (Frequently Asked Questions)**

**What are horizontal curves in road design?**

Horizontal curves are bends in the road alignment that allow vehicles to smoothly change direction. They are essential for ensuring safe navigation around obstacles or changes in terrain.

**What types of horizontal curves exist?**

There are seven main types of horizontal curves:

- Simple Curve
- Compound Curve
- Reverse Curve
- Transition Curve
- Lemniscate Curve
- Spiral Curve
- Cubic Parabolic Curve

**What is a vertical curve and where is it used?**

Vertical curves are changes in road gradient designed to accommodate changes in terrain elevation. They are crucial in mountainous regions and where roads need to transition between uphill and downhill slopes.

**What are the types of vertical curves?**

There are two types of vertical curves:

- Summit Curve (convexity upward)
- Valley Curve or Sag Curve (convexity downward)

**What is the purpose of a transition curve?**

A transition curve is used to smoothly transition the alignment of a road from straight to curved or vice versa, reducing discomfort for passengers and allowing vehicles to maintain safe speeds.

**How do horizontal curves impact road safety?**

Horizontal curves ensure vehicles can navigate bends safely, reducing the risk of accidents by providing a gradual change in direction.

**Why are compound curves used in road design?**

Compound curves combine multiple radii to navigate complex terrain or to avoid obstacles, allowing for efficient road layout without extensive earthwork.

**Where are valley curves most commonly applied?**

Valley curves, also known as sag curves, are typically used in locations where the road dips into a lower terrain, managing the transition smoothly while accounting for gravitational forces acting on vehicles.

**What considerations are made when designing summit curves?**

Summit curves are designed to accommodate the upward centrifugal force, ensuring passenger comfort and safety while accounting for sight distances necessary for overtaking and stopping.

**How do vertical curves reduce earthwork in road construction?**

Vertical curves allow roads to smoothly transition between different elevations, minimizing the need for extensive excavation or filling, thus reducing construction costs and environmental impact.