Important Point

## 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 it’s called a horizontal curve.

When the curves are provided with some vertical elevation, then it’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

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## 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.

Also, Read: What Is Contour Interval | Calculation of Contour Intervals | Uses of Contour Intervals in Surveying

### 5. Lemniscate Curve

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

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

**L = C√sin ^{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

Also, Read: Benchmark in Surveying | TBM in Surveying | GTS Benchmark| Permanent Benchmark| Arbitrary Benchmark

## 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 that’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.

Also, Read: Principle of Plane Table Surveying Methods | Equipment | Error | Advantage | Limitation

## 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; that’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.

### What Are Horizontal Curves?

**Horizontal Curves** are one of the two important transition elements in geometric design for highways (along with Vertical **Curves**). A **horizontal curve** provides a transition between two tangent strips of roadway, allowing a vehicle to negotiate a turn at a gradual rate rather than a sharp cut.

### Types of Horizontal Curves

**Simple Curve:**A simple arc provided in the road to impose a curve between the two straight lines.**Compound Curve:**Combination of two simple curves combined together to curve in the same direction.**Reverse Curve:**Combination of two simple curves combined together to curve in the same direction.**Transition or Spiral Curve:**A curve that has a varying radius. Its provided with a simple curve and between the simple curves in a compound curve.

### What Are Vertical Curves?

A **vertical curve** provides a transition between two sloped roadways, allowing a vehicle to negotiate the elevation rate change at a gradual rate rather than a sharp cut. These **curves** are parabolic and are assigned stationing based on a horizontal axis.

### Types of Vertical Curves

**Sag Curves and****Crest Curves.**

Sag curves are used where the change in grade is positive, such as valleys, while crest curves are used when the change in grade is negative, such as hills.

### Application of Curves

While algebraic **curves** traditionally have provided a path toward modern algebraic geometry, they also provide many **applications** in number theory, computer security and cryptography, coding theory, differential equations, and more.

### Vertical Curve Formulas Surveying

Ease of computation of **vertical** offsets, which permits easily computed **curve** elevations. The slope of this **curve** at any point is given by the first derivative, dy/dx = 2ax + b The rate of change of slope is given by the second derivative, d2y/dx2 = 2a 2a is a constant.

### Horizontal Curves Surveying

A **horizontal curve** provides a transition between two tangent strips of roadway, allowing a vehicle to negotiate a turn at a gradual rate rather than a sharp cut. These **curves** are semicircles as to provide the driver with a constant turning rate with radii determined by the laws of physics surrounding centripetal force.

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