# Curve Surveying

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**Classify Curves**1**Define the following terms: i. Back and Forward Tangent ii. Point of Intersection iii. Point of Curve iv. Point of Tangency v. Intersection angle and Deflection angle vi. Tangent distance and External distance**2**Describe the Curve Designation**3**Recall the Elements of Simple Curve**3**Recall Linear methods of Setting out Simple Curves: i. By Ordinates from Long Chord ii. By Bisection of Arc iii. By Offsets from Tangent iv. By Offsets from Chord Produced**4**Recall the Rankine’s Method of Deflection Angle**5**Recall the Two Theodolite Method**6**Recall the Tacheometer Method**7**Recall the Elements of Compound Curve**8**Describe the relationship between Parts of Compound Curve**9**Recall the Process of Setting Out the Compound Curve**10**Recall the Elements of Reverse Curve**11**Describe the Relationship between Parts of Reverse Curve**12

Classify Curves

Curves in surveying are used to describe the shape of a road, a railway line, or other features that change direction continuously. There are several different types of curves used in surveying, including:

- Simple Curves: These are curves that have a constant radius throughout their length. Simple curves are used when the change in direction of the feature being surveyed is gradual and uniform.
- Compound Curves: These are curves that have two or more simple curves with different radii joined together. Compound curves are used when the change in direction of the feature being surveyed is not uniform and requires a combination of curves with different radii.
- Reverse Curves: These are curves that change direction twice in a short distance. Reverse curves are used when the feature being surveyed changes direction quickly and then returns to its original direction.
- Transition Curves: These are curves that are used to provide a smooth transition between straight sections of a feature and curved sections. Transition curves are used to prevent sudden changes in direction that could cause discomfort or safety concerns for users of the feature.
- Spiral Curves: These are curves that have a continuously changing radius. Spiral curves are used to provide a gradual transition between straight sections of a feature and curved sections, or to provide a smooth transition between two curves with different radii.

Each type of curve has a specific equation that describes its shape, and surveying instruments and methods are used to measure and calculate the parameters of the curve, such as radius and central angle. The choice of the type of curve to use in a particular surveying project depends on the characteristics of the feature being surveyed and the goals of the survey.

Define the following terms: i. Back and Forward Tangent ii. Point of Intersection iii. Point of Curve iv. Point of Tangency v. Intersection angle and Deflection angle vi. Tangent distance and External distance

i. Back and Forward Tangent: The back tangent and forward tangent are the straight lines that are tangent to a curve at its starting and ending points respectively.

ii. Point of Intersection: The point of intersection is where two or more curves meet or intersect.

iii. Point of Curve: The point of curve is the point on the curve where a change in direction occurs.

iv. Point of Tangency: The point of tangency is the point where a straight line touches a curve without crossing it.

v. Intersection angle and Deflection angle: The intersection angle is the angle between the two intersecting lines or curves at the point of intersection. The deflection angle is the change in direction of a curve as it moves from one tangent to another.

vi. Tangent distance and External distance: The tangent distance is the distance along the curve between two points of tangency. The external distance is the direct distance between two points on the curve, without following the curve.

Describe the Curve Designation

The curve designation is a method used to identify and label the different parts of a curve in a transportation or surveying project. It involves assigning names and symbols to different parts of a curve such as the beginning, end, center, or any specific point on the curve.

The designation of a curve typically includes the name or symbol of the curve, the degree of curvature, the radius of the curve, the length of the curve, and the central angle of the curve. This information is used to properly design the curve and to ensure that it meets the requirements and specifications of the project.

For example, a typical curve designation may be “Curve C-2, R = 500 ft, L = 1000 ft, θ = 60°”. This designation means that the curve is referred to as “Curve C-2”, has a radius of 500 feet, a length of 1000 feet, and a central angle of 60 degrees.

By having a clear and standardised method of curve designation, engineers and surveyors can easily communicate and understand the specifications and characteristics of a particular curve.

Recall the Elements of Simple Curve

It refers to the recall of the elements of a simple curve. A simple curve is a type of curve in surveying and geometrics that is defined by its geometric elements. The following are the main elements of a simple curve:

- Radius: The radius of a curve is the distance from the center of the curve to its point of tangency.
- Arc Length: The arc length is the length of the curved path of the simple curve, which can be calculated using the formula 2πr x (central angle/360°).
- Chord Length: The chord length is the straight-line distance between two points on the curve.
- Central Angle: The central angle is the angle formed by two radii at the center of the curve.
- Length of Tangent: The length of the tangent is the straight-line distance from the point of tangency to the center of the curve.
- Point of Intersection: The point of intersection is the intersection point between the curve and the tangent.
- Point of Curve: The point of curve is a point on the curved path of the simple curve.
- Point of Tangency: The point of tangency is the point where the curve touches the tangent.
- Intersection Angle: The intersection angle is the angle between the chord and the tangent at the point of intersection.
- Deflection Angle: The deflection angle is the angle between the tangent and the chord at the point of tangency.

Recall Linear methods of Setting out Simple Curves: i. By Ordinates from Long Chord ii. By Bisection of Arc iii. By Offsets from Tangent iv. By Offsets from Chord Produced

The four methods are:

i. By Ordinates from Long Chord: This method involves finding ordinates from a long chord and using them to set out the points of the curve. A long chord is drawn between two points on the curve, and the ordinates are taken at equal intervals along the chord. The curve is then set out by drawing perpendiculars from the ordinates to the curve.

ii. By Bisection of Arc: In this method, the arc is divided into a number of equal parts and perpendiculars are drawn from the midpoints of the divisions to the curve. The points where the perpendiculars intersect the curve are then marked.

iii. By Offsets from Tangent: This method involves finding the offsets from the tangent, that is, the perpendicular distances from the curve to a line tangent to the curve at a given point. The offsets are taken at equal intervals along the tangent and the curve is set out by drawing perpendiculars from the offsets to the curve.

iv. By Offsets from Chord Produced: This method involves finding the offsets from a chord produced, that is, a line extended from a chord of the curve. The offsets are taken at equal intervals along the chord produced, and the curve is set out by drawing perpendiculars from the offsets to the curve.

Recall the Rankine’s Method of Deflection Angle

Rankine’s Method of Deflection Angle is a linear method used to find the deflection angle in a simple curve. It is based on the principle that the deflection angle of a simple curve is equal to the angle between the tangent and the chord of the curve. The method requires the length of the chord and the radius of the curve to be known.

The deflection angle is then calculated using the formula:

Δ = 2 * arctan(C / 2R)

Where Δ is the deflection angle, C is the length of the chord and R is the radius of the curve. The method is simple and straightforward, making it a popular choice for setting out simple curves. However, it is important to note that this method is only applicable for simple curves and may not be suitable for compound or reverse curves.

Recall the Two Theodolite Method

The Two Theodolite Method is a surveying technique used to determine the relative position of two points in space. It involves using two theodolites, each of which is a type of surveying instrument that measures angles and distances to determine the position of a target.

The process of the Two Theodolite Method involves the following steps:

- Setting up the first theodolite at a known point and pointing it towards a reference point (target).
- Measuring the angle and distance to the reference point with the first theodolite.
- Moving the second theodolite to the reference point and pointing it towards the first theodolite.
- Measuring the angle and distance from the reference point to the first theodolite with the second theodolite.
- Using the measured angles and distances to calculate the relative position of the two points.

The result of the Two Theodolite Method is a set of relative coordinates that describe the position of one point with respect to the other. This information can be used to determine the location of a target in space, or to determine the relative position of two objects in order to compare their position and orientation.

Overall, the Two Theodolite Method is a useful and accurate method for determining the relative position of two points, and it is widely used in surveying and engineering applications.

Recall the Tacheometer Method

The Tacheometer Method, also known as the Stadia Method, is a surveying technique used to determine the distance and height of objects. It is similar to the Two Theodolite Method, but involves the use of a tacheometer, which is a specialised surveying instrument that can quickly measure distances and heights.

The process of the Tacheometer Method involves the following steps:

- Setting up the tacheometer at a known point and pointing it towards the object whose height and distance is to be measured.
- Measuring the angle to the top and bottom of the object with the tacheometer.
- Calculating the height and distance to the object using the angle measurements and the tacheometer’s internal scales.

The Tacheometer Method is a quick and efficient way to determine the height and distance of objects, as the tacheometer can measure angles and distances very quickly and accurately. This method is often used in engineering and construction applications, as well as in surveying and mapping.

One of the key benefits of the Tacheometer Method is its ability to measure heights and distances without having to physically touch the object. This allows the surveyor to accurately measure the height and distance of objects that are difficult to reach or that would be damaged if touched, such as trees, tall buildings, and other structures.

Overall, the Tacheometer Method is an important tool in the field of surveying, as it provides a fast and accurate way to determine the height and distance of objects.

Recall the Elements of Compound Curve

A compound curve is a type of curved alignment in surveying and transportation engineering that consists of two or more curves of different radii joined together. It is used to provide a smooth transition between two straight lines or two other curves, and is often used in the design of highways, railway tracks, and other transportation systems.

The elements of a compound curve include:

- Point of Compound Curve (PCC): This is the point at which two curves of different radii meet and change direction.
- Back Tangent: This is the straight line segment that connects the PCC to the start of the first curve.
- Curve 1: This is the first curve of the compound curve, which starts at the PCC and extends to the Point of Reverse Curve (PRC).
- Point of Reverse Curve (PRC): This is the point at which the first curve ends and the second curve begins.
- Reverse Curve: This is the second curve of the compound curve, which starts at the PRC and extends to the Forward Tangent.
- Forward Tangent: This is the straight line segment that connects the end of the second curve to the next point in the alignment.

The design of a compound curve involves determining the appropriate radii for the two curves, as well as the length of the back tangent and forward tangent. This is done to ensure that the compound curve provides a smooth transition between the two straight lines or curves and that the alignment meets the design criteria for the transportation system.

Overall, the compound curve is an important element in the design of transportation systems, as it provides a smooth transition between different alignments and allows for the safe and efficient flow of traffic.

Describe the relationship between Parts of Compound Curve

A compound curve is composed of several parts that work together to provide a smooth transition between two straight lines or curves. These parts include the Point of Compound Curve (PCC), the Back Tangent, Curve 1, the Point of Reverse Curve (PRC), the Reverse Curve, and the Forward Tangent.

The relationship between these parts of a compound curve is as follows:

- Point of Compound Curve (PCC): The PCC is the starting point of the compound curve and the point at which the two curves of different radii meet and change direction. It marks the transition from the straight line to the curved alignment.
- Back Tangent: The Back Tangent connects the PCC to the start of the first curve. Its length determines the rate at which the alignment changes direction and is designed to provide a smooth transition into the first curve.
- Curve 1: Curve 1 is the first curve of the compound curve and starts at the PCC. Its radius determines the rate at which the alignment changes direction and its length is determined based on the design criteria for the transportation system.
- Point of Reverse Curve (PRC): The PRC is the end point of the first curve and the starting point of the second curve. It marks the transition from the first curve to the second curve.
- Reverse Curve: The Reverse Curve is the second curve of the compound curve and starts at the PRC. Its radius determines the rate at which the alignment changes direction and its length is determined based on the design criteria for the transportation system.
- Forward Tangent: The Forward Tangent connects the end of the second curve to the next point in the alignment. Its length determines the rate at which the alignment changes direction and is designed to provide a smooth transition into the next alignment.

In summary, the relationship between the parts of a compound curve is such that each part works together to provide a smooth and efficient transition between two alignments. The length and radius of each part is carefully designed based on the design criteria for the transportation system, to ensure a safe and efficient flow of traffic.

Recall the Process of Setting Out the Compound Curve

The process of setting out a compound curve in surveying involves several steps to ensure that the curve is accurately and precisely positioned in the field. The following outlines the general steps in the process of setting out a compound curve:

- Determine Design Parameters: The first step is to determine the design parameters for the compound curve, including the radii of the two curves, the lengths of the back and forward tangents, and the location of the Point of Compound Curve (PCC) and Point of Reverse Curve (PRC).
- Establish Control Points: The next step is to establish control points that will be used to set out the compound curve in the field. This typically involves setting up a series of control points along the straight lines that connect the PCC and PRC, as well as at the PCC and PRC themselves.
- Set Out Back Tangent: Once the control points have been established, the next step is to set out the back tangent. This involves using a measuring tape or other surveying equipment to measure the length of the back tangent and marking the starting point of the first curve.
- Set Out Curve 1: The next step is to set out Curve 1. This typically involves using a theodolite or tacheometer to measure the radius of the first curve and determine its center point. From the center point, surveyors use a measuring tape or other equipment to measure out to the Point of Reverse Curve (PRC).
- Set Out Reverse Curve: Once the PRC has been established, the next step is to set out the reverse curve. This involves using a theodolite or tacheometer to measure the radius of the second curve and determine its center point. From the center point, surveyors use a measuring tape or other equipment to measure out to the forward tangent.
- Set Out Forward Tangent: The final step is to set out the forward tangent. This involves using a measuring tape or other surveying equipment to measure the length of the forward tangent and marking the end point of the compound curve.

In conclusion, setting out a compound curve involves a series of steps to accurately and precisely position the curve in the field. The process requires a combination of surveying equipment and manual measurement, as well as careful consideration of the design parameters for the curve.

Recall the Elements of Reverse Curve

A reverse curve is a type of curved alignment that changes direction twice, allowing for a smooth transition between two straight lines or other curves. The elements of a reverse curve include:

- Point of Reverse Curve (PRC): The PRC is the starting point of the reverse curve and the point at which the two curves of different radii meet and change direction. It marks the transition from the straight line or first curve to the second curve.
- Reverse Curve 1: Reverse Curve 1 is the first curve of the reverse curve and starts at the PRC. Its radius determines the rate at which the alignment changes direction and its length is determined based on the design criteria for the transportation system.
- Reverse Curve 2: Reverse Curve 2 is the second curve of the reverse curve and starts at the end of Reverse Curve 1. Its radius determines the rate at which the alignment changes direction and its length is determined based on the design criteria for the transportation system.
- Forward Tangent: The Forward Tangent connects the end of the second curve to the next point in the alignment. Its length determines the rate at which the alignment changes direction and is designed to provide a smooth transition into the next alignment.

In summary, the elements of a reverse curve are the Point of Reverse Curve (PRC), Reverse Curve 1, Reverse Curve 2, and Forward Tangent. Each element works together to provide a smooth and efficient transition between two alignments, with the length and radius of each curve determined based on the design criteria for the transportation system.

Describe the Relationship between Parts of Reverse Curve

The different parts of a reverse curve in surveying are all interconnected and work together to create a smooth and efficient transition between two alignments. The relationship between the parts of a reverse curve can be described as follows:

- Point of Reverse Curve (PRC) and Reverse Curves 1 & 2: The PRC marks the transition from one alignment to the next and is the starting point of the reverse curves. Reverse Curve 1 and Reverse Curve 2 are connected to the PRC and work together to change the direction of the alignment. The length and radius of Reverse Curve 1 and Reverse Curve 2 are determined based on the design criteria for the transportation system, and work together to provide a smooth transition between the two alignments.
- Reverse Curves 1 & 2 and Forward Tangent: Reverse Curve 1 and Reverse Curve 2 change the direction of the alignment and connect to the Forward Tangent. The length of the Forward Tangent is designed to provide a smooth transition into the next alignment, and is determined based on the design criteria for the transportation system.
- Reverse Curves 1 & 2 and Alignments: Reverse Curve 1 and Reverse Curve 2 connect the two alignments, changing the direction of the alignment as it transitions from one to the other. The length and radius of each curve are designed to provide a smooth and efficient transition between the two alignments.

In conclusion, the parts of a reverse curve in surveying are all connected and work together to create a smooth and efficient transition between two alignments. The Point of Reverse Curve (PRC), Reverse Curves 1 & 2, and Forward Tangent all play a crucial role in determining the direction and smoothness of the alignment, with their length and radius determined based on the design criteria for the transportation system.