Curves are used in transportation routes to gradually change direction between straight segments. There are several types of curves including simple, compound, reverse, and transition curves. A simple circular curve connects two tangents with a single arc, and is defined by its radius or degree. Transition curves provide a gradual transition between tangents and circular curves to avoid abrupt changes in grade or superelevation that could cause vehicles to overturn. There are several methods for laying out circular curves, including using offset distances from the long chord between tangent points or measuring deflection angles from the initial tangent.
This document discusses methods for setting out simple circular curves in surveying. There are two main methods: linear and angular.
The linear method uses only a tape or chain and does not require angle measurement. It includes setting out curves by offsets from the long chord, by successive bisection of arcs, and by offsets from the tangents.
The angular method is used for longer curves and involves measuring deflection angles. It includes Rankine's method of tangential angles using a tape and theodolite to measure deflection angles from the back tangent to points on the curve. The two theodolite method also uses angle measurement between two theodolites.
1) Curves are gradual bends provided in transportation infrastructure like roads, railways and canals to allow for a smooth change in direction or grade.
2) There are two main types of curves - horizontal curves which provide a gradual change in direction, and vertical curves which provide a gradual change in grade.
3) Curves are needed to safely guide vehicles and traffic when changing directions or grades, to improve visibility, and to prevent erosion of canal banks from water pressure.
This document summarizes methods for setting out simple circular curves based on linear and angular methods. The linear methods discussed are by offsets from the long chord, successive bisection of arcs, offsets from tangents, and offsets from chords produced. The angular methods discussed are Rankine's method of tangential angles, the two theodolite method, and the tacheometric method. Each method is briefly described in one or two sentences.
This document provides information about circular curves used in highways and railways. It discusses the different types of curves including simple, compound, and reverse curves. It defines key elements of circular curves such as radius, deflection angle, tangent length, and mid-ordinate. It presents the relationships between radius and degree of curvature. Finally, it describes various methods for setting out circular curves in the field, including linear methods using offsets and angular methods using a theodolite.
Tacheometric surveying uses a tacheometer to determine horizontal and vertical distances through angular measurements. A tacheometer is a theodolite fitted with stadia hairs and an anallatic lens. The tacheometric formula relates the staff intercept, focal length, stadia interval and additive constant to calculate horizontal distances. Methods include stadia, fixed/movable hair, and non-stadia techniques. Determining the tacheometer constant involves measuring distances and staff intervals at stations to solve equations. Errors arise from incorrect stadia intervals or graduations. Tacheometric surveying provides distances in rough terrain but with less precision than other methods.
Tacheometric surveying is a method of rapidly determining horizontal and vertical positions of points using optical measurements rather than traditional tape or chain measurements. A tacheometer, which is a transit theodolite fitted with a stadia diaphragm, is used to measure the horizontal and vertical angles to a stadia rod or staff held at survey points. Formulas involving the stadia interval, staff intercept readings, and calculated constants are used to determine horizontal distances and elevations from the instrument to points. Measurements can be taken with horizontal lines of sight or inclined lines of sight when the staff is held vertically or normal to the line of sight.
This document describes different methods of trigonometric leveling to determine the elevation of points. Trigonometric leveling uses vertical angles measured with a theodolite and distances to calculate elevations. There are methods to determine elevations when the base is accessible and inaccessible, and when instrument stations and objects are in the same or different vertical planes. Calculations use trigonometric functions and relationships between angles and distances in triangles formed by the instrument stations and object.
Tacheometric surveying is a method of surveying that determines horizontal and vertical distances optically rather than through direct measurement with a tape or chain. It uses an instrument called a tacheometer fitted with a stadia diaphragm to rapidly measure distances. The key principles are that the ratio of perpendicular to base is constant in similar triangles, allowing horizontal distance and elevation to be calculated from observed angles and staff intercept readings. Common tacheometric systems include fixed hair stadia, subtense stadia, and tangential methods. Distance and elevation formulas are derived for horizontal, inclined, and depressed line of sights depending on staff orientation. Tacheometric surveying is well-suited for difficult terrain where direct measurement is challenging
This document discusses methods for setting out simple circular curves in surveying. There are two main methods: linear and angular.
The linear method uses only a tape or chain and does not require angle measurement. It includes setting out curves by offsets from the long chord, by successive bisection of arcs, and by offsets from the tangents.
The angular method is used for longer curves and involves measuring deflection angles. It includes Rankine's method of tangential angles using a tape and theodolite to measure deflection angles from the back tangent to points on the curve. The two theodolite method also uses angle measurement between two theodolites.
1) Curves are gradual bends provided in transportation infrastructure like roads, railways and canals to allow for a smooth change in direction or grade.
2) There are two main types of curves - horizontal curves which provide a gradual change in direction, and vertical curves which provide a gradual change in grade.
3) Curves are needed to safely guide vehicles and traffic when changing directions or grades, to improve visibility, and to prevent erosion of canal banks from water pressure.
This document summarizes methods for setting out simple circular curves based on linear and angular methods. The linear methods discussed are by offsets from the long chord, successive bisection of arcs, offsets from tangents, and offsets from chords produced. The angular methods discussed are Rankine's method of tangential angles, the two theodolite method, and the tacheometric method. Each method is briefly described in one or two sentences.
This document provides information about circular curves used in highways and railways. It discusses the different types of curves including simple, compound, and reverse curves. It defines key elements of circular curves such as radius, deflection angle, tangent length, and mid-ordinate. It presents the relationships between radius and degree of curvature. Finally, it describes various methods for setting out circular curves in the field, including linear methods using offsets and angular methods using a theodolite.
Tacheometric surveying uses a tacheometer to determine horizontal and vertical distances through angular measurements. A tacheometer is a theodolite fitted with stadia hairs and an anallatic lens. The tacheometric formula relates the staff intercept, focal length, stadia interval and additive constant to calculate horizontal distances. Methods include stadia, fixed/movable hair, and non-stadia techniques. Determining the tacheometer constant involves measuring distances and staff intervals at stations to solve equations. Errors arise from incorrect stadia intervals or graduations. Tacheometric surveying provides distances in rough terrain but with less precision than other methods.
Tacheometric surveying is a method of rapidly determining horizontal and vertical positions of points using optical measurements rather than traditional tape or chain measurements. A tacheometer, which is a transit theodolite fitted with a stadia diaphragm, is used to measure the horizontal and vertical angles to a stadia rod or staff held at survey points. Formulas involving the stadia interval, staff intercept readings, and calculated constants are used to determine horizontal distances and elevations from the instrument to points. Measurements can be taken with horizontal lines of sight or inclined lines of sight when the staff is held vertically or normal to the line of sight.
This document describes different methods of trigonometric leveling to determine the elevation of points. Trigonometric leveling uses vertical angles measured with a theodolite and distances to calculate elevations. There are methods to determine elevations when the base is accessible and inaccessible, and when instrument stations and objects are in the same or different vertical planes. Calculations use trigonometric functions and relationships between angles and distances in triangles formed by the instrument stations and object.
Tacheometric surveying is a method of surveying that determines horizontal and vertical distances optically rather than through direct measurement with a tape or chain. It uses an instrument called a tacheometer fitted with a stadia diaphragm to rapidly measure distances. The key principles are that the ratio of perpendicular to base is constant in similar triangles, allowing horizontal distance and elevation to be calculated from observed angles and staff intercept readings. Common tacheometric systems include fixed hair stadia, subtense stadia, and tangential methods. Distance and elevation formulas are derived for horizontal, inclined, and depressed line of sights depending on staff orientation. Tacheometric surveying is well-suited for difficult terrain where direct measurement is challenging
1) Levelling is the process of determining the relative elevations of points on or near the earth's surface. It is important for engineering projects to determine elevations along alignments.
2) Levelling is used to prepare contour maps, determine altitudes, and create longitudinal and cross sections needed for projects.
3) Key terms include bench mark, datum, reduced level, line of collimation, and height of instrument. Different types of levelling include simple, differential, fly, longitudinal, and cross-sectional levelling.
Tacheometry is a surveying method that uses optical instruments like a theodolite fitted with a stadia diaphragm to measure horizontal and vertical distances between points. It works on the principle that the ratio of distance from the instrument to the base of an isosceles triangle and the length of the base is constant. Distances are calculated using stadia intercept readings and multiplying constants based on the focal length of the instrument's objective lens. Tacheometry offers faster measurement compared to traditional chaining and is useful for surveys in difficult terrain like rivers, valleys, or undulating ground where conventional surveying would be inaccurate or slow.
Surveying Engineering
Traversing Practical part 1
Plane and Applied surveying 2
Report number(2)
• Report name :Gales Traverse Table(Horizontal angle
measurement (FL)of closed traversing
• Apparatus
• Theodolite Instrument
• Tripod
• Compass
• Pin
• Tape
• Range pole
Object
• To conducted survey work in a closed traversing and calculate
in depend coordinates and area calculation by coordinate rule.
Procedure Traverse;
Calculations Traverse .Dada Sheet and Table method work clock wise surveying
-Gales Traverse Table.
*Traverse Calculations
-Traverse Calculation.
-Coordinate conversions.
-Signs of Departures and Latitudes.
*Balancing latitude and departure
-Correction for ∆E& ∆N:
Bowditch adjustment or compass method
-The example…
-Vector components (pre-adjustment)
*The adjustment components
Prepared by:
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
The document provides information about theodolite surveying including:
1. A theodolite is an instrument used to measure horizontal and vertical angles which can also be used to prolong lines, measure distances indirectly, and for leveling.
2. Theodolite traversing involves establishing control points by measuring angles and distances between traverse stations to calculate positions.
3. Components of a theodolite include a telescope that can rotate vertically and a compass to determine direction, along with accessories like a tripod, rods, and tapes used in surveying.
The document discusses theodolite traversing and defines key terms related to using a transit theodolite. It describes the main components of a transit theodolite including the telescope, vertical circle, plate bubbles, tribrach, and foot screws. It explains how to perform temporary adjustments like centering the theodolite over a station mark and leveling it using the tripod and foot screws. It also provides details on measuring horizontal and vertical angles with a vernier theodolite.
This document provides information about tacheometry, which is a method of surveying that determines horizontal and vertical distances from instrumental observations. It discusses how tacheometry can be used when obstacles make traditional surveying difficult. The key aspects covered include:
- Defining tacheometry and the measurements it provides
- When tacheometry is advantageous over other surveying methods
- The instruments used, including tacheometers and levelling rods
- How horizontal and vertical distances are calculated using constants
- The different types of tacheometer diaphragms and telescopes
- The fixed hair method for taking readings
The document discusses different types of traverses and methods for conducting traverse surveys. It describes two types of traverses: open traverses that begin and end at points of known and unknown positions, and closed traverses that begin and end at points of known positions, including closed-loop traverses that begin and end at the same point. It also outlines four methods for determining directions during traversing: chain angle method, free needle method, fast needle method, and measuring angles between lines. Finally, it discusses instruments used for measuring angles like compasses and theodolites, and defines different types of bearings including true, magnetic, and arbitrary bearings.
This document discusses the use of a theodolite for surveying. It begins by explaining that a theodolite is needed to precisely measure horizontal and vertical angles, unlike a compass. It then defines theodolite surveying as surveying that measures angles using a theodolite. The document goes on to classify theodolites based on their horizontal axis and method of angle measurement. It describes the basic parts of a transit vernier theodolite and explains terms used in manipulating one. Finally, it discusses methods for measuring horizontal angles, including the general, repetition, and reiteration methods.
1. Levelling is used to determine the relative heights of points and establish a common datum. It involves using a level instrument and staff to obtain precise elevation readings.
2. Key terms include benchmarks, backsight, foresight, and intermediate sight readings. Common level instruments are the dumpy level, tilting level, wye level, and automatic level.
3. Levelling methods include simple, differential, fly, check, profile, cross, and reciprocal levelling used for different applications such as construction works. Precise setup and focusing of the instrument are required before taking readings.
Edm is a surveying instrument used to measure the distance electronically. This Surveying Instrument is used in triangulation to measure the length of Base line because more accuracy is required to measure the length of base line.
This document describes three methods for measuring horizontal angles with a theodolite:
1) Ordinary Method: A horizontal angle is measured between points A and B by sighting each point and recording the vernier readings. The process is repeated by changing instrument faces and the average of readings gives the angle.
2) Repetition Method: A more accurate method where the angle is mechanically added several times by repeatedly sighting point A after sighting B.
3) Reiteration Method: Several angles are measured successively at a station, closing the horizon by resighting the initial point. Any error is distributed among the measured angles.
This document discusses triangulation, which is a surveying technique used to establish horizontal control networks over large areas. It involves measuring angles and lengths within networks of triangles. There are different orders of triangulation based on accuracy and area covered, including primary, secondary, and tertiary triangulation. Key aspects discussed include triangulation station layout and design, angle and distance measurements, controlling errors, and computation of unknown lengths and directions within triangles.
Trilateration and triangulation are surveying methods to establish horizontal control networks. Trilateration involves measuring the lengths of all three sides of triangles without measuring angles, while triangulation measures angles and the length of one base line. Both methods are used to determine coordinate positions through trigonometric computations. Triangulation networks can be classified based on their intended accuracy and purpose, from primary/first order for determining large areas to tertiary/third order for more detailed surveys.
Compass surveying involves measuring directions of survey lines using a magnetic compass and measuring lengths using a chain or tape. It is used when the area is large, undulating and has many details. In compass surveying, a series of connected lines are established through traversing. The magnetic bearing of each line is measured using a prismatic compass or surveyor's compass, and the distance is measured using a chain. Compass surveying is recommended for large and undulating areas without suspected magnetic interference. The key principles are measuring bearings using a compass and distances using a chain to establish connected lines through traversing without requiring triangulation.
This document discusses various methods for computing the area of irregular shapes from field notes and plotted plans in surveying. It describes graphical, instrumental, and computational methods using the trapezoidal rule, mid-ordinate rule, average ordinate rule, and Simpson's rule. Specific steps are outlined for computing area from field notes by dividing the shape into triangles, rectangles, squares, and trapezoids. Methods for computing area from a plotted plan include dividing the shape into triangles using bases and altitudes, counting squares of a known unit area, or drawing parallel lines to form rectangles.
1. The document provides information on theodolite traversing and describes the parts and functions of a transit vernier theodolite. It discusses how to set up the theodolite over a station and level it up, which are important temporary adjustments.
2. The theodolite is used to measure horizontal and vertical angles precisely and for various surveying applications. It has parts like the telescope, vertical circle, standards, and upper and lower plates.
3. Proper temporary adjustments of the theodolite include setting it up over a station point using a plumb bob, and then leveling the instrument using plate levels and levelling screws.
Metric Chain : It Consists of galvanized mild steel wire of 4mm diameter known as link.
It is available in 20m, 30m, 50m length which consists of 100 links.
Gunter’s Chain : A 66 feet long chain consists of 100 links, each of 0.66 feet, it is known as Gunter’s chain.
This chain is suitable for taking length in miles.
Engineer’s Chain : A 100 feet long chain consisting of 100 links each of 1 feet is known as engineer’s chain.
This chain is used to measure length in feet and area in sq.yard.
Revenue Chain : it is 33 feet long chain consisting of 16 links.
This chain is used for distance measurements in feet & inches for smaller areas.
This document discusses the use of a theodolite for surveying. It begins by explaining that a theodolite is needed to precisely measure horizontal and vertical angles, unlike a compass. It then defines theodolite surveying as surveying that measures angles using a theodolite. The document goes on to classify theodolites based on their horizontal axis and method of reading angles. It describes the basic parts of a transit vernier theodolite and explains terms used in manipulating one. Finally, it discusses methods for measuring horizontal angles, including the general, repetition, and reiteration methods.
Theodolite traversing, purpose and principles of theodolite traversingDolat Ram
The document discusses theodolite traversing, which is a surveying method that uses a theodolite to measure angles and a chain or tape to measure distances between control points called traverse stations.
The theodolite is used to measure horizontal and vertical angles, and there are two main types - optical and electronic digital theodolites. The chain or tape is used to measure distances between traverse stations.
A traverse consists of straight lines connecting traverse stations, with known lengths and angles defined by theodolite measurements. Traverses can be open or closed loops. Theodolite traversing is used for area computation, surveying, data reduction, and indirect measurement of elevations, distances, and
i) Curves are used in transportation lines like roads, railways and canals to provide gradual changes in direction and grade instead of abrupt turns. They are classified as horizontal or vertical based on the plane they operate in.
ii) A simple circular curve consists of a single arc of a circle connecting two straight lines or tangents. It is designated by its radius or degree, which indicates the sharpness of the curve.
iii) Curves are set out through linear methods using chains and tapes or angular instrumental methods. This involves locating the tangent points and laying out pegs along the curve at set intervals to join and form the curved alignment.
This document provides definitions and explanations of terms related to horizontal curves. It discusses the following:
- Horizontal curves are used to connect two straight lines when there is a change in direction of a road or railway alignment. Circular curves are the most common type of horizontal curve.
- Key terms defined include degree of curve, radius, relationship between radius and degree, superelevation, and centrifugal ratio.
- Different types of horizontal curves are described, including simple circular, compound, reverse, and transition curves.
- Notation used in circular curves is explained, such as tangent points and lengths, deflection angle, and radius.
- Properties of simple circular curves are outlined, including
1) Levelling is the process of determining the relative elevations of points on or near the earth's surface. It is important for engineering projects to determine elevations along alignments.
2) Levelling is used to prepare contour maps, determine altitudes, and create longitudinal and cross sections needed for projects.
3) Key terms include bench mark, datum, reduced level, line of collimation, and height of instrument. Different types of levelling include simple, differential, fly, longitudinal, and cross-sectional levelling.
Tacheometry is a surveying method that uses optical instruments like a theodolite fitted with a stadia diaphragm to measure horizontal and vertical distances between points. It works on the principle that the ratio of distance from the instrument to the base of an isosceles triangle and the length of the base is constant. Distances are calculated using stadia intercept readings and multiplying constants based on the focal length of the instrument's objective lens. Tacheometry offers faster measurement compared to traditional chaining and is useful for surveys in difficult terrain like rivers, valleys, or undulating ground where conventional surveying would be inaccurate or slow.
Surveying Engineering
Traversing Practical part 1
Plane and Applied surveying 2
Report number(2)
• Report name :Gales Traverse Table(Horizontal angle
measurement (FL)of closed traversing
• Apparatus
• Theodolite Instrument
• Tripod
• Compass
• Pin
• Tape
• Range pole
Object
• To conducted survey work in a closed traversing and calculate
in depend coordinates and area calculation by coordinate rule.
Procedure Traverse;
Calculations Traverse .Dada Sheet and Table method work clock wise surveying
-Gales Traverse Table.
*Traverse Calculations
-Traverse Calculation.
-Coordinate conversions.
-Signs of Departures and Latitudes.
*Balancing latitude and departure
-Correction for ∆E& ∆N:
Bowditch adjustment or compass method
-The example…
-Vector components (pre-adjustment)
*The adjustment components
Prepared by:
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
The document provides information about theodolite surveying including:
1. A theodolite is an instrument used to measure horizontal and vertical angles which can also be used to prolong lines, measure distances indirectly, and for leveling.
2. Theodolite traversing involves establishing control points by measuring angles and distances between traverse stations to calculate positions.
3. Components of a theodolite include a telescope that can rotate vertically and a compass to determine direction, along with accessories like a tripod, rods, and tapes used in surveying.
The document discusses theodolite traversing and defines key terms related to using a transit theodolite. It describes the main components of a transit theodolite including the telescope, vertical circle, plate bubbles, tribrach, and foot screws. It explains how to perform temporary adjustments like centering the theodolite over a station mark and leveling it using the tripod and foot screws. It also provides details on measuring horizontal and vertical angles with a vernier theodolite.
This document provides information about tacheometry, which is a method of surveying that determines horizontal and vertical distances from instrumental observations. It discusses how tacheometry can be used when obstacles make traditional surveying difficult. The key aspects covered include:
- Defining tacheometry and the measurements it provides
- When tacheometry is advantageous over other surveying methods
- The instruments used, including tacheometers and levelling rods
- How horizontal and vertical distances are calculated using constants
- The different types of tacheometer diaphragms and telescopes
- The fixed hair method for taking readings
The document discusses different types of traverses and methods for conducting traverse surveys. It describes two types of traverses: open traverses that begin and end at points of known and unknown positions, and closed traverses that begin and end at points of known positions, including closed-loop traverses that begin and end at the same point. It also outlines four methods for determining directions during traversing: chain angle method, free needle method, fast needle method, and measuring angles between lines. Finally, it discusses instruments used for measuring angles like compasses and theodolites, and defines different types of bearings including true, magnetic, and arbitrary bearings.
This document discusses the use of a theodolite for surveying. It begins by explaining that a theodolite is needed to precisely measure horizontal and vertical angles, unlike a compass. It then defines theodolite surveying as surveying that measures angles using a theodolite. The document goes on to classify theodolites based on their horizontal axis and method of angle measurement. It describes the basic parts of a transit vernier theodolite and explains terms used in manipulating one. Finally, it discusses methods for measuring horizontal angles, including the general, repetition, and reiteration methods.
1. Levelling is used to determine the relative heights of points and establish a common datum. It involves using a level instrument and staff to obtain precise elevation readings.
2. Key terms include benchmarks, backsight, foresight, and intermediate sight readings. Common level instruments are the dumpy level, tilting level, wye level, and automatic level.
3. Levelling methods include simple, differential, fly, check, profile, cross, and reciprocal levelling used for different applications such as construction works. Precise setup and focusing of the instrument are required before taking readings.
Edm is a surveying instrument used to measure the distance electronically. This Surveying Instrument is used in triangulation to measure the length of Base line because more accuracy is required to measure the length of base line.
This document describes three methods for measuring horizontal angles with a theodolite:
1) Ordinary Method: A horizontal angle is measured between points A and B by sighting each point and recording the vernier readings. The process is repeated by changing instrument faces and the average of readings gives the angle.
2) Repetition Method: A more accurate method where the angle is mechanically added several times by repeatedly sighting point A after sighting B.
3) Reiteration Method: Several angles are measured successively at a station, closing the horizon by resighting the initial point. Any error is distributed among the measured angles.
This document discusses triangulation, which is a surveying technique used to establish horizontal control networks over large areas. It involves measuring angles and lengths within networks of triangles. There are different orders of triangulation based on accuracy and area covered, including primary, secondary, and tertiary triangulation. Key aspects discussed include triangulation station layout and design, angle and distance measurements, controlling errors, and computation of unknown lengths and directions within triangles.
Trilateration and triangulation are surveying methods to establish horizontal control networks. Trilateration involves measuring the lengths of all three sides of triangles without measuring angles, while triangulation measures angles and the length of one base line. Both methods are used to determine coordinate positions through trigonometric computations. Triangulation networks can be classified based on their intended accuracy and purpose, from primary/first order for determining large areas to tertiary/third order for more detailed surveys.
Compass surveying involves measuring directions of survey lines using a magnetic compass and measuring lengths using a chain or tape. It is used when the area is large, undulating and has many details. In compass surveying, a series of connected lines are established through traversing. The magnetic bearing of each line is measured using a prismatic compass or surveyor's compass, and the distance is measured using a chain. Compass surveying is recommended for large and undulating areas without suspected magnetic interference. The key principles are measuring bearings using a compass and distances using a chain to establish connected lines through traversing without requiring triangulation.
This document discusses various methods for computing the area of irregular shapes from field notes and plotted plans in surveying. It describes graphical, instrumental, and computational methods using the trapezoidal rule, mid-ordinate rule, average ordinate rule, and Simpson's rule. Specific steps are outlined for computing area from field notes by dividing the shape into triangles, rectangles, squares, and trapezoids. Methods for computing area from a plotted plan include dividing the shape into triangles using bases and altitudes, counting squares of a known unit area, or drawing parallel lines to form rectangles.
1. The document provides information on theodolite traversing and describes the parts and functions of a transit vernier theodolite. It discusses how to set up the theodolite over a station and level it up, which are important temporary adjustments.
2. The theodolite is used to measure horizontal and vertical angles precisely and for various surveying applications. It has parts like the telescope, vertical circle, standards, and upper and lower plates.
3. Proper temporary adjustments of the theodolite include setting it up over a station point using a plumb bob, and then leveling the instrument using plate levels and levelling screws.
Metric Chain : It Consists of galvanized mild steel wire of 4mm diameter known as link.
It is available in 20m, 30m, 50m length which consists of 100 links.
Gunter’s Chain : A 66 feet long chain consists of 100 links, each of 0.66 feet, it is known as Gunter’s chain.
This chain is suitable for taking length in miles.
Engineer’s Chain : A 100 feet long chain consisting of 100 links each of 1 feet is known as engineer’s chain.
This chain is used to measure length in feet and area in sq.yard.
Revenue Chain : it is 33 feet long chain consisting of 16 links.
This chain is used for distance measurements in feet & inches for smaller areas.
This document discusses the use of a theodolite for surveying. It begins by explaining that a theodolite is needed to precisely measure horizontal and vertical angles, unlike a compass. It then defines theodolite surveying as surveying that measures angles using a theodolite. The document goes on to classify theodolites based on their horizontal axis and method of reading angles. It describes the basic parts of a transit vernier theodolite and explains terms used in manipulating one. Finally, it discusses methods for measuring horizontal angles, including the general, repetition, and reiteration methods.
Theodolite traversing, purpose and principles of theodolite traversingDolat Ram
The document discusses theodolite traversing, which is a surveying method that uses a theodolite to measure angles and a chain or tape to measure distances between control points called traverse stations.
The theodolite is used to measure horizontal and vertical angles, and there are two main types - optical and electronic digital theodolites. The chain or tape is used to measure distances between traverse stations.
A traverse consists of straight lines connecting traverse stations, with known lengths and angles defined by theodolite measurements. Traverses can be open or closed loops. Theodolite traversing is used for area computation, surveying, data reduction, and indirect measurement of elevations, distances, and
i) Curves are used in transportation lines like roads, railways and canals to provide gradual changes in direction and grade instead of abrupt turns. They are classified as horizontal or vertical based on the plane they operate in.
ii) A simple circular curve consists of a single arc of a circle connecting two straight lines or tangents. It is designated by its radius or degree, which indicates the sharpness of the curve.
iii) Curves are set out through linear methods using chains and tapes or angular instrumental methods. This involves locating the tangent points and laying out pegs along the curve at set intervals to join and form the curved alignment.
This document provides definitions and explanations of terms related to horizontal curves. It discusses the following:
- Horizontal curves are used to connect two straight lines when there is a change in direction of a road or railway alignment. Circular curves are the most common type of horizontal curve.
- Key terms defined include degree of curve, radius, relationship between radius and degree, superelevation, and centrifugal ratio.
- Different types of horizontal curves are described, including simple circular, compound, reverse, and transition curves.
- Notation used in circular curves is explained, such as tangent points and lengths, deflection angle, and radius.
- Properties of simple circular curves are outlined, including
Curves are used in transportation routes to provide a gradual change in direction between straight segments. There are several types of curves including simple, compound, and reverse curves. Curves are necessary to avoid obstacles, reduce grading costs, and make alignments more comfortable for transportation. Curves are set out using various linear and angular methods involving measurement of offsets, chords, or angles from tangent lines or radii. Common linear methods include setting offsets perpendicular to chords or tangents drawn from the curve center.
This document discusses curves used in transportation routes. It defines different types of curves including simple, compound, and reverse curves. It provides the nomenclature and key elements of simple circular curves, such as tangents, points of intersection and tangency, deflection angle, chord length, arc length, and mid-ordinate. The document also discusses the designation and degree of curves, and describes methods for setting out curves using linear measurements or angular measurements along the curve. Sample problems are provided to demonstrate how to calculate elements of a simple circular curve given radius, deflection angle, and chainage information.
Curves are used to gradually change the direction of transportation routes like roads, railways and pipelines. They connect straight tangents and are usually circular arcs. There are different types of curves classified based on their shape and connection of tangents like simple, compound, reverse etc. Elements like radius, deflection angle, length of curve, tangent length etc are used to design circular curves. Various surveying methods like Rankine's, two theodolite etc are used to establish curves on the ground based on their elements and principles. Compound curves consist of two simple circular curves bending in the same direction and joining at a common point of compound.
This document discusses simple circular curves, which are curves consisting of a single arc with a constant radius connecting two tangents. It defines key elements of circular curves such as deflection angle, radius of curvature, chord length, and tangent length. Circular curves are used to impose curves between two straight lines in roads and railways. The document also discusses designating curves by their degree or radius, with degree defined as the angle subtended by a 30m chord at the curve's center. Fundamental geometry rules for circular curves are provided.
The document discusses circular curves and their use in highway and railway alignment. It defines key terms related to circular curves like deflection angle, chord, radius, and introduces different types of horizontal curves - simple circular curves, compound curves, reverse curves, spiral curves, and lemniscate curves. It also discusses vertical curves like valley and summit curves. The document provides formulas to calculate length of tangent, external distance, middle ordinate, length of chord, length of curve, degree of curve, and minimum radius of curvature for circular curves. It includes examples of problems calculating radius, offset distance, and degree of curve given different curve elements.
Introduction, classification of curves, Elements of a simple circular, designation of curve, methods of setting out a simple circular curve, elements of a compound and reverse curves, transition curve, types of transition curves, combined curve, types of vertical curves
This document discusses horizontal curves in surveying. It covers the objectives of learning about horizontal curve layout, types of curves like simple, compound, and reverse curves. It defines degree of curve and how it is calculated based on the arc or cord length. It describes the elements of a circular curve like point of curvature, point of tangency, radius, chord length, and central angle. Methods for laying out a circular curve are discussed, including linear methods using offsets and bisection, and angular methods like Rankine's method and two theodolite method. Key questions about why curves are needed and defining the degree of curve are also answered.
Location horizontal and vertical curves Theory Bahzad5
Setting out of works
horizontal and vertical curves
Horizontal Alignment
ØAn introduction to horizontal curve &Vertical curve.
ØTypes of curves.
ØElements of horizontal circular curve.
ØGeometric of circular curve
Ø Methods of setting out circular curve
Ø Setting out of horizontal curve on ground
Ø Vertical curve Definition.
ØElements of the vertical curves.
ØAvailable methods for computing the elements of vertical curves
Types of Curves
1- Horizontal Curves
2- Vertical Curves
Horizontal Curves
are circular curves. They connect tangent lines around
obstacles, such as building, swamps, lakes, change
direction in rural areas, and intersections in urban areas.
-Compound Curve.
-Reverse curve.
-Transition or Spiral Curves.
-Horizontal Curve: Simple circular
curve
-Elements of horizontal curves.
-Formulas for simple circular
curves.
-Properties of circular curves.
example:A horizontal curve having R= 500m, ∆=40°, station P.I=
12+00 ,prepare a setting out table to set out the curve
using deflection angle from the tangent and chord length
method, dividing the arc into 50m stations.
:Example H.W
A Horizontal curve is designed with a 600m radius and is
known to have a tangent of 52 m the PI is Station
200+00 determent the Stationing of the PT?
-PROCEDURE SETTING OUT Practical .
Vertical Curves
Elevation and Stations of main points on the Vertical Curve .
Assumptions of vertical curve projection.
Example: A vertical parabola curve 400m long is to be set
between 2% (upgrade) and 1% (down grade), which meet
at chainage of 2000 m, the R.L of point of intersection of
the two gradients being (500.00 m). Calculate the R.L of
the tangent and at every (50m) parabola.
Thank you all
Prepared by:
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
This document discusses horizontal curves used in transportation infrastructure to gradually change the direction of roads, railways, and other linear structures. It defines simple, compound, and reverse circular curves used for this purpose. Simple curves are arcs of a circle defined by their radius, while compound curves consist of two simple curves joined together curving in the same direction. Reverse curves curve in opposite directions. Spiral curves with varying radii are also used. The document then provides details on calculating elements of simple circular curves like radius, tangent distance, external distance, middle ordinate, and degree of curvature using standard geometric relationships. It concludes with describing the deflection angle method for laying out horizontal curves in the field using one or two theodolites.
The document discusses setting out curves for highways. It defines different types of curves, including horizontal and vertical curves. Horizontal curves can be circular, transition, or lemniscate curves. Vertical curves connect different gradients and can be circular arcs or parabolic arcs. Common elements of circular curves are defined, such as tangents, points of intersection, and long chords. Methods for setting out simple circular curves include linear methods using offsets from long chords, bisection of arcs, tangents, or chords produced.
This document provides information on surveying circular curves. It defines different types of curves including simple, compound, and reverse curves. It also defines various curve elements such as point of intersection, point of curve, point of tangency, radius, and deflection angle. Methods for designating a curve by radius or degree of curvature are presented along with relationships between these values. Formulas are given for calculating the length of a curve, tangent length, length of chord, external distance, and mid-ordinate based on the radius and deflection angle. Finally, linear and angular methods for setting out a simple circular curve in the field are described.
Overview:
The vertical alignment of a road consists of gradients(straight lines in a vertical plane) and vertical curves. The vertical alignment is usually drawn as a profile, which is a graph with elevation as vertical axis and the horizontal distance along the centre line of the road as the the horizontal axis.
This presentation constitutes an integral component of a designated course curriculum and is crafted and disseminated for its intended audience. None of the contents within this presentation should be construed as a formal publication on the subject matter. The author has extensively referenced published resources in the preparation of this presentation, and proper citations will be provided in the bibliography upon completion of its development.
The document discusses different types of curves used in civil engineering projects including roads, railways, and canals. It defines simple, compound, reverse, and deviation curves. Simple curves consist of a single circular arc connecting two straight lines, while compound curves use two or more arcs of different radii bending in the same direction. Reverse curves use two arcs bending in opposite directions. Terminology for curve surveying is also outlined, and linear methods for laying out simple circular curves are described, including offsets from the long chord, radial offsets from tangents, and perpendicular offsets from tangents. The document provides examples to calculate curve parameters and set out a curve given information like the deflection angle, tangent distance, and radius.
The document discusses different types of curves used in transportation and infrastructure projects. It describes horizontal curves and vertical curves, which provide gradual changes in direction and grade. Curves are needed on roads, railways, and canals to allow vehicles to transition between paths meeting at an angle, as well as to facilitate gradual changes in elevation and improve visibility and safety. The document outlines key elements of horizontal curves, including the point of intersection, deflection angle, radius, point of curvature, point of tangency, and length of curve.
Curves are usually fitted to tangents by choosing a D (degree of curve) that will place the centerline of the curve on
or slightly on or above the gradeline. Sometimes D is chosen to satisfy a limited tangent distance or a desired curve
length. Each of these situations is discussed below:
Choosing D to fit a gradeline (the most common case).
When joining two tangents where the centerline of the curve is to fall on or slightly above the gradeline,
the desired external is usually used to select D.
This document provides information about curve ranging in surveying engineering. It begins with describing the expected learning outcomes of understanding how to calculate positions for horizontal and vertical curves. It then discusses different types of horizontal curves used in road and railway design, including simple, compound, transition and reverse curves. The key geometry and elements of circular curves like tangent length, external distance, mid-ordinate and curve length are defined. Several example problems are provided to show how to tabulate data and calculate values needed to lay out horizontal and vertical curves using surveying methods and tools. Vertical curves called summit and valley curves are also introduced to smoothly connect changes in roadway gradients.
The document discusses remote sensing, GPS, and GIS. It defines remote sensing as collecting information about terrain or objects from a distance without physical contact. Remote sensing uses electromagnetic radiation of different wavelengths, which interact with the atmosphere and Earth's surface. GPS is a satellite-based navigation system that allows devices to determine their precise location. It consists of 24 satellites, ground control stations, and user receivers. Receivers use signals from multiple satellites to calculate their position, velocity, and time. GPS field surveys involve setting up receivers and antennas to take height and location measurements.
1. The document discusses advanced surveying equipment that provide more precise and faster surveying compared to traditional methods. It describes the Electronic Distance Meter (EDM), microoptic theodolite, electronic/digital theodolite, and total station.
2. An EDM measures distance using the phase difference between a transmitted and reflected wave. A microoptic theodolite and electronic theodolite are used to measure angles precisely.
3. A total station integrates EDM and theodolite functions to allow simultaneous distance and angle measurements for surveying tasks such as setting out buildings, contour mapping, and more.
This document provides information on theodolite surveying. It discusses how to measure the magnetic bearing of a line, prolong and range a line, measure deflection angles, vertical angles, and includes steps for closed and open traverse surveys using the included angle and deflection angle methods. It also covers topics like observation tables, consecutive and independent coordinates, and balancing a traverse using Bowditch's rule and the transit rule.
Theodolite surveying part 1 (I scheme MSBTE)Naufil Sayyad
The document provides information about theodolite surveying. It defines a theodolite as an instrument used to measure horizontal and vertical angles accurately. The main types of theodolites are described based on the type of telescope and reading unit. The key components of a transit theodolite are identified and explained. Methods for measuring horizontal angles using a transit theodolite via the direct and repetition methods are outlined, including how to set up the instrument, take readings, and calculate angles.
This document discusses theodolite surveying. It defines a theodolite as an instrument used to accurately measure horizontal and vertical angles. The document outlines the components of a theodolite and different types including transit, non-transit, vernier, micrometer, digital/electronic, and optic theodolites. It also defines various technical terms used in theodolite surveying such as swinging, transiting, face left, face right, and changing face. The main uses and functions of a theodolite are to measure horizontal and vertical angles, magnetic bearings, deflection angles, horizontal distances, and elevations.
Plane table surveying is a graphical surveying method where field work and plotting are done simultaneously without the use of a field book. The key accessories of a plane table setup include the plane table, alidade, spirit level, trough compass, and U-fork with plumb bob. There are three main methods used - radiation, intersection, and traversing. Some benefits are that it is a rapid method, errors can be easily detected, and irregular objects can be accurately represented. However, it is not suitable for highly accurate work or in inclement weather conditions.
How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
Brand Guideline of Bashundhara A4 Paper - 2024khabri85
It outlines the basic identity elements such as symbol, logotype, colors, and typefaces. It provides examples of applying the identity to materials like letterhead, business cards, reports, folders, and websites.
How to Setup Default Value for a Field in Odoo 17Celine George
In Odoo, we can set a default value for a field during the creation of a record for a model. We have many methods in odoo for setting a default value to the field.
Information and Communication Technology in EducationMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 2)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐈𝐂𝐓 𝐢𝐧 𝐞𝐝𝐮𝐜𝐚𝐭𝐢𝐨𝐧:
Students will be able to explain the role and impact of Information and Communication Technology (ICT) in education. They will understand how ICT tools, such as computers, the internet, and educational software, enhance learning and teaching processes. By exploring various ICT applications, students will recognize how these technologies facilitate access to information, improve communication, support collaboration, and enable personalized learning experiences.
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐫𝐞𝐥𝐢𝐚𝐛𝐥𝐞 𝐬𝐨𝐮𝐫𝐜𝐞𝐬 𝐨𝐧 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐞𝐭:
-Students will be able to discuss what constitutes reliable sources on the internet. They will learn to identify key characteristics of trustworthy information, such as credibility, accuracy, and authority. By examining different types of online sources, students will develop skills to evaluate the reliability of websites and content, ensuring they can distinguish between reputable information and misinformation.
How to Create a Stage or a Pipeline in Odoo 17 CRMCeline George
Using CRM module, we can manage and keep track of all new leads and opportunities in one location. It helps to manage your sales pipeline with customizable stages. In this slide let’s discuss how to create a stage or pipeline inside the CRM module in odoo 17.
2. INTRODUCTION
Curves are usually employed in lines of communication
in order that the change of direction at the intersection
of the straight line shall be gradual.
The lines connected by the curves are tangential to it
and are called as tangents or straights.
3. NECESSITY
Excessive cutting and filling can be prevented by providing the change in
alignment by curves.
The obstruction which came in the way of straight alignment can be
made easier by providing by pass with the help of curves
In the straight route gradient are made more comfortable and easy
providing diversions with help of curves
In the straight route costly land comes in the way then it can avoided by
providing diversions with the help of curves.
5. SIMPLE CIRCULAR CURVE
Simple circular curve consists of
single arc connecting two
tangents or straight.
Simple curve is normally
represented by the length of its
radius or by the degree of curve
6. COMPOUND CURVE
A compound curve consist of two
arcs of different radii curving in the
same direction and lying on the
same side of their common
tangent , their centers being on
the same side of the curve.
7. REVERSE CURVE
A reverse curve is composed of two
arcs of equal or different radii
bending or curving in opposite
direction with common tangent at
their junction, their centers being in
opposite sides of the curve.
8. TRANSITION CURVE
A curve of varying radius is known as ‘transition curve’.
The radius of such curve varies from infinity to certain
fixed value. A transition curve is provided on both ends
of the circular curve. The transition curve is also called
as spiral or easement curve.
9.
10.
11. OBJECTIVES OF PROVIDING TRANSITION CURVE
To accomplish gradually the transition from the tangent to the
circular curve, and from the circular curve to the tangent.
To obtain a gradual increase of curvature from zero at the
tangent point to the specified quantity at the junction of the
transition curve with the circular curve.
To provide the super elevation gradually from zero at the
tangent point to the specified amount on the circular curve
To avoid the overturning of the vehicle.
12. REQUIREMENTS OF IDEAL TRANSITION CURVE
It should meet the original straight
tangentially
It should meet the circular curve
tangentially
Its radius at the junction with the circular
curve should be the same as that of the
circular curve
The rate of increase of curvature along
the transition curve should be same as
that of in increase of superelevation
The length should be such that the full
superelevation is attained at the junction
with the circular curve
13. LAMNISCATE CURVE
It is mostly used in roads when it is required to have curve
transitional throughout having no intermediate circular curve
Since the curve is symmetrical and transitional throughout the
super elevation or cant continuously increases till the apex is
reached
This may be objectionable in case of railways
14. REASONS OF PROVIDING LAMNISCATE CURVE IN ROADS
Its radius of curvature decreases more
gradually than circular curve
Its rate of increase of curvature
diminishes towards the transition curve
thus fulfilling the essential condition
It corresponds to the autogenous curve
of vehicle(i.e. the path actually traced
by vehicle when running freely)
17. DEGREE OF CURVE
The angle subtended at the
center of the circle by a chord
of standard length of 30m is
known as degree of curve.
18. Referring Fig
Let R = the radius of the curve in m.
D = the degree of curve.—
MN = the chord 30 m long.
P = Mid point of chord MN
In triangle OMP, OM = R,
PM = ½MN = 15 m.
Then sin D/2 = PM/OM = 15/R
Or R = 15(Exact)
Sin D/2
RELATION BETWEEN RADIUOS AND DEGREE OF CURVE
19. RELATION BETWEEN RADIUOS AND DEGREE OF CURVE
When D is small, sin D/2 = D/2 radians
R= 15/((D/2)x (Л/180))
R=15/ (ЛD/360)
R= 15x360/ ЛD
R= 1718.89/D
R= 1719/D
20. NOTATIONS USED IN SIMPLE CIRCULAR CURVE
1. The straight lines AB and BC, which are
connected by the curve are called the
tangents or straights to the curve.
2. The point B at which the two tangent lines AB
and BC intersect is known as the point of
intersection (P.I.) or the vertex (V).
3. If the curve deflects to the right of direction of
progress of survey (AB), it is called as right hand
curve, if to the left , it is called as left hand curve.
21. NOTATIONS USED IN SIMPLE CIRCULAR CURVE
4. The tangent line AB is called the first tangent
or rear tangent (also called the back tangent)
The tangent line BC is called as the second
tangent or forward tangent.
5. The points (T1 and T2) at which the curve
touches the straights are called tangent
point(T.P.).
6. The beginning of the curve (T1) Is called the
point of curve.(P.C.) or the tangent curve (T.C.).
The end of the curve (T2) is known as the point
of tangency(P.T.) or the curve tangent(C.T.).
22. NOTATIONS USED IN SIMPLE CIRCULAR CURVE
7. The ےABC between the tangent lines AB and
BC is called the angle of intersection (I). The
ےB'BC (i.e. the angle by which the forward
tangent deflects from the rear tangent) is known
as the deflection angle (ø) of the curve.
8. The distance from the point of intersection to
the tangent point is called the tangent distance
or tangent length.
(BT1 and BT2).
9. The line T1T2 joining the two point (T1 and
T2) is known as the long chord.(L).
23. NOTATIONS USED IN SIMPLE CIRCULAR CURVE
10.The arc T1FT2 is called the length of the
curve.(l).
11.The mid point F of the arc T1FT2 is known as
the apex or the summit of the curve and lies on
the bisector of the angle of the intersection.
12. The distance BF from the point of the
intersection to the apex of the curve is called the
apex distance of external distance.
24. NOTATIONS USED IN SIMPLE CIRCULAR CURVE
13.The angle T1OT2 subtended at the centre of
curve by the arc T1FT2 is known as the central
angle, and is equal to the deflection angle.(ø)
14.The intercept EF on the line OB between the
apex (F) of the curve and the midpoint (E) of the
long chord is called the versed sine of the curve.
25. ELEMENTS OF SIMPLE CIRCULAR CURVE
T1BT2 + B’BT2 = 1800 or I + Ø =1800 ……….…(1)
The angle T1OT2 = 1800 - I = Ø ……………(2)
Tangent length = BT1 = BT2 = OT1 tan(Ø/2) = R
tan(Ø/2) … ..(4)
Length of the chord (L) = 2T1E = 2OT1 sin
(Ø/2)=2R sin (Ø/2)…(5)
Length of the curve(l) = length of the arc T1FT2
= R X Ø (in radians) = ЛR Ø/180°
26. ELEMENTS OF SIMPLE CIRCULAR CURVE
If the curve be designated by the degrees of the
curve(D),
Length of the curve =(30 Ø)/D (30 m chord)
………….(6a)
= (20 Ø)/D (20 m chord) ………....(6b) Apex
distance = BF = BO – OF = OT1 sec (Ø/2) – OF
27. ELEMENTS OF SIMPLE CIRCULAR CURVE
Versed sine of the curve = EF = OF – OE=OF –
OT1 COS(Ø/2)
28. Peg interval :-
It is the usual practice to fix pegs at equal intervalon the curve
as along the straight.
The interval between the peg is usually 20 to 30 m. strictly
speaking this interval must be measured as the arch intercept
between them.
However as it is necessarily measured along the chord, the
curve consist of series of a chord rather than of arcs. In other
words, the length of the chord is assume to be equal to be that
of the arc.
29. Peg interval :-
In order that the difference in length between the arc and
chord may be negligible, the length of the chord should not be
more than 1/20th of the radius of the curve.
The length of unit chord (peg interval) is,therefore, 30m for
flat curve, 20m for sharp curve, and 10 m or less for very sharp
curve.
When the curve is of a small radius, the peg interval are
considered to be along the arc and the length of the
corresponding chords are calculated to locate the pegs.
30. METHODS OF SETTING OUT SIMPLE CIRCULAR CURVE
LINEAR METHOD
ANGULAR METHOD
OFFSET FROM LONG
CHORD METHOD
RANKINE’SMETHOD OF
DEFLECTION ANGLE
31. OFFSET FROM LONG CHORD METHOD
Let AB and BC = the tangents to the
curve T1DT2
T1 and T2 = tangent points T1T2 = the
long chord of length L.
ED = O0 = the offsets at the midpoint
of T1T2 (the versed sine) PQ = Ox = the
offsets at a distance x from E so that
EP = x OT1 = OT2 = OD = R = The radius
of the curve.
33. OFFSET FROM LONG CHORD METHOD
Given data: Direction of two straights,
chainage of point of intersection,
radius of curve.
Procedure:
1. Set theodolite over B and measure
deflection angle Ф
2. Calculate tangent length by formula
R x tan (ϕ/2).
34. OFFSET FROM LONG CHORD METHOD
3. Locate first tangent T1 point by
measuring backward along BA distance
equal to tangent length and second
tangent point T2 by measuring forward
along BC distance equal to tangent
length.
4. Divide long chord into even number
of equal parts.
5. Calculate ordinates O0 by formula
O0 = R – (R2-(L/2)2)0.5 and other
ordinates by formula Ox = (R2-X2)0.5 –
(R- O0).
35. OFFSET FROM LONG CHORD METHOD
6. Locate mid point of long chord (
point E)
7. Chain is laid in ET1 direction;
perpendicular is erected at E, and says
by optical square, point on curve is
fixed by measuring distance O0 along
the erected perpendicular.
8. Other offsets are similarly set.
9. Curve being similar about midpoint
of long chord, calculations for right
half are similar to left half.
36. RANKINE’S METHOD OF DEFLECTION ANGLE
In this method the curve is set out by
the tangential angles(often called the
deflection angles) with a theodolite
and a chain or tape.
37. RANKINE’S METHOD OF DEFLECTION ANGLE
The derivation of the formula for
calculating the deflection angle it as
fallows :-
Let,
AB = the rear tangent to the curve.
T1 and T2 = the tangent points
D,E,F, etc. = the successive points on
the curve.
δ1, δ2,δ3, etc = the tangential angles
which each of the successive chord
T1D, DE. EF etc makes with the
respective tangents at T1, D, E, etc.
38. RANKINE’S METHOD OF DEFLECTION ANGLE
∆1,∆2,∆3, etc = the total tangential or
deflection angles
(between the rear tangent AB and
each of the lines T1D, DE, EF, etc.
c1,c2,c3 etc = the lengths of the chord
T1D, DE, EF, etc. R = radius of the curve
Chord T1D = arc T1D (very small ) = c1.
39. RANKINE’S METHOD OF DEFLECTION ANGLE
Similarly, and so on.
BT1D = δ1 =½ T1OD i.e. T1D = 2δ1 NOW,
40. RANKINE’S METHOD OF DEFLECTION ANGLE
Hence,
Since the chord lengths c2, c3, …….cn-
1 is equal to the length of the unit
chord (peg interval), δ2=δ3= δ4= δn-1.
Now, the total tangential (deflection)
angle (∆1) for the first chord
(T1D) = BT1D
Therefore
∆1 = δ1
41. RANKINE’S METHOD OF DEFLECTION ANGLE
The total tangential angle (∆2) for the
second chord (DE) =BT1E.
But BT1E = BT1D + DT1E.
Now the angle DT1E is the angle
subtended by the chord DE in the
opposite segment and therefore,
equals the tangential angle (δ2)
between the tangent at D and the
chord DE.
42. RANKINE’S METHOD OF DEFLECTION ANGLE
Therefore, ∆2 = δ1 + δ2 = ∆1 + δ2
Similarly, ∆3 = δ1 + δ2 + δ3 = ∆2 +
δ3
∆n = δ1 + δ2 + δ3+………... + δn
∆n = ∆n-1 + δn
Check;- The total deflection angle
(BT1T2) = ∆n = ( ø/2 ) where ø is
the deflection angle of the curve.
From the above, it will be seen that
the deflection angle (∆) for any chord
is equal to the deflection angle for
preceding chord plus the tangential
angle for the chord
43. RANKINE’S METHOD OF DEFLECTION ANGLE
If the degree of the curve (D) be given,
the deflection angle for 30m chord is
equal to ½ D degrees, and that for the
sub chord is equal to (c1×D)/60
degrees,
where c1 is the length of the first
chord
45. RANKINE’S METHOD OF DEFLECTION ANGLE
Procedure:-
To set out a curve
i. Set up the theodolite over first
tangent point (T1) and level it.
ii. With both plates clamped at zero,
direct the telescope to the ranging rod
at the point of intersection B and
bisect it.
iii. Release the vernier plate and set
the vernier A to first deflection angle
(∆1), the telescope being thus directed
along T1D.
46. RANKINE’S METHOD OF DEFLECTION ANGLE
vi. Pin down the zero end of the chain
or tape at T1, and holding the arrow at
the distance on the chain equal to the
length of the first chord, swing the
chain around T1 until the arrow is
bisected by the cross-hairs, thus fixing
the first point D on the curve.
v. Unclamp the upper plate and set the
vernier to the second deflection angle
∆2, the line of sight bring now directed
along T1E.
47. RANKINE’S METHOD OF DEFLECTION ANGLE
vi. Hold the zero end of the chain at D
and swing the other end around D
until the arrow held at other end is
bisected by the line of sight , thus
locating the second point on the
curve.
vii. Repeat the process until the end of
the curve is reached.
48. RANKINE’S METHOD OF DEFLECTION ANGLE
Check:-
The last point thus located must
coincide with the previously located
tangent point T2. If not, find the
distance between them which is actual
error.
If it is within the permissible limit, the
last few pegs may be adjusted, if it is
exceeds the limit, the entire work
must be checked.