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 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
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.
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
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 discusses different methods for balancing a closed traverse survey by distributing corrections to station coordinates. It provides examples of using Bowditch's Rule, the Transit Rule, and the Third Rule to balance a sample traverse with given length, latitude, and departure coordinates. Bowditch's Rule distributes corrections proportionally to leg lengths, while the Transit Rule uses angular precision assumptions and the Third Rule separates corrections between northings/southings and eastings/westings.
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.
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 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
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.
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
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 discusses different methods for balancing a closed traverse survey by distributing corrections to station coordinates. It provides examples of using Bowditch's Rule, the Transit Rule, and the Third Rule to balance a sample traverse with given length, latitude, and departure coordinates. Bowditch's Rule distributes corrections proportionally to leg lengths, while the Transit Rule uses angular precision assumptions and the Third Rule separates corrections between northings/southings and eastings/westings.
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.
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.
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 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.
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.
The document provides information about theodolites. It begins with an introduction stating that a theodolite is used to measure horizontal and vertical angles more precisely than a magnetic compass. It then discusses the main parts of a theodolite including the horizontal circle, vertical circle, telescope, and levels. The document also covers the history of theodolites from their early origins to modern electronic versions. It describes how to operate a transit vernier theodolite including terms like centering, transiting, swinging the telescope, and changing face. Finally, it discusses the permanent and temporary adjustments needed to ensure accurate theodolite measurements.
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.
Plane table surveying involves simultaneously conducting fieldwork and plotting on a drawing board equipped with a ball and socket leveling arrangement. An alidade, which is a ruler with a fiducial edge and sighting frames, is used to draw lines of sight. A telescopic alidade can take inclined sights to increase range and accuracy. Orientation is achieved through resection or backsight methods. The radiation, intersection, traversing, and resection plane table methods are used to connect stations and fill in surveyed details on the map.
1. The document presents information from a slideshow on tacheometric surveying. It discusses various methods of tacheometric surveying including fixed hair, movable hair, tangential, and subtense bar methods.
2. Formulas are provided for calculating horizontal distance, vertical distance, and elevation of points using these different tacheometric surveying methods under various sighting conditions such as inclined or depressed lines of sight.
3. The document also discusses tacheometric constants, anallatic lenses, and procedures for conducting field work in a tacheometric survey including selecting instrument stations, taking observations of vertical angles and staff readings, and shifting to subsequent stations.
This document discusses contouring and contour maps. It defines a contour line as a line connecting points of equal elevation. The vertical distance between consecutive contours is called the contour interval, which depends on factors like the nature of the ground and the map scale. Contour maps show the topography of an area and can be used for engineering projects, route selection, and estimating earthworks. Methods of plotting contours include direct methods using levels or hand levels, and indirect methods like gridding, cross-sectioning, and radial lines. Characteristics of contours provide information about the landscape.
Introduction, electromagnetic spectrum, electromagnetic distance measurement, types of EDM instruments, electronic digital theodolites, total station, digital levels, scanners for topographical survey, global positioning system.
Leveling is a surveying technique used to determine differences in elevation between points. It involves measuring vertical distances between a fixed benchmark and other points using a leveling instrument, leveling rod, and trigonometric leveling. There are two main methods for leveling - the height of instrument method and rise and fall method. Leveling is used to establish elevations, construct contour maps, and determine cut/fill volumes for engineering projects.
1. Levelling is used to determine relative heights and elevations of points and establish points at required elevations. It involves using instruments like levels and staffs.
2. There are different types of levels (dumpy, tilting, wye, automatic) and staffs (self-reading, target). Precise levelling is done to establish permanent benchmarks.
3. Adjustments must be made to level instruments during setup and permanently. Methods like differential, profile and cross levelling are used depending on the task. Reciprocal levelling involves backsight-foresight exchange to check for errors.
This document provides an overview of tacheometric surveying. It discusses the principles and methods of tacheometry including the stadia, fixed hair, movable hair, and tangential methods. Formulas are provided for calculating horizontal distance, vertical distance, and elevation using each method. The key principles are that tacheometry uses trigonometric relationships based on intercepts measured through a stadia diaphragm to determine horizontal and vertical distances between instrument and target stations.
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.
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.
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.
This document is a field report for a traversing survey conducted by students. It contains unadjusted and average field data from three separate traverses, including measured horizontal and vertical angles between stations. It also shows the calculations to determine angular errors, angle adjustments, course bearings, latitudes and departures, adjusted coordinates, and station positions. The objectives, equipment used, and results are presented in tables and graphs.
Tacheometric surveying is a method that determines horizontal and vertical distances optically rather than using a tape or chain. It uses a theodolite fitted with a stadia diaphragm containing hairs to rapidly measure distances. There are different systems, including the stadia system which uses fixed or movable hairs, and the tangential system. Formulas are used to calculate distances and elevations based on staff intercept readings and vertical angles observed. The constants of the instrument such as the multiplying constant and additive constant must also be determined.
Tacheometric surveying is a method of surveying that uses optical instruments to rapidly measure horizontal and vertical distances between points. It is well-suited for difficult terrain where direct measurements with tapes or chains are impossible. A tacheometer, which is a theodolite fitted with a stadia diaphragm, is used to measure the angle subtended by a known distance on a stadia rod or staff at a point. This allows the horizontal distance and elevation of points to be calculated trigonometrically without direct measurement. Common tacheometric methods include fixed hair stadia, subtense, and tangential systems. Field procedures involve establishing instrument stations along a traverse and taking angular and stadia rod readings
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 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.
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.
The document provides information about theodolites. It begins with an introduction stating that a theodolite is used to measure horizontal and vertical angles more precisely than a magnetic compass. It then discusses the main parts of a theodolite including the horizontal circle, vertical circle, telescope, and levels. The document also covers the history of theodolites from their early origins to modern electronic versions. It describes how to operate a transit vernier theodolite including terms like centering, transiting, swinging the telescope, and changing face. Finally, it discusses the permanent and temporary adjustments needed to ensure accurate theodolite measurements.
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.
Plane table surveying involves simultaneously conducting fieldwork and plotting on a drawing board equipped with a ball and socket leveling arrangement. An alidade, which is a ruler with a fiducial edge and sighting frames, is used to draw lines of sight. A telescopic alidade can take inclined sights to increase range and accuracy. Orientation is achieved through resection or backsight methods. The radiation, intersection, traversing, and resection plane table methods are used to connect stations and fill in surveyed details on the map.
1. The document presents information from a slideshow on tacheometric surveying. It discusses various methods of tacheometric surveying including fixed hair, movable hair, tangential, and subtense bar methods.
2. Formulas are provided for calculating horizontal distance, vertical distance, and elevation of points using these different tacheometric surveying methods under various sighting conditions such as inclined or depressed lines of sight.
3. The document also discusses tacheometric constants, anallatic lenses, and procedures for conducting field work in a tacheometric survey including selecting instrument stations, taking observations of vertical angles and staff readings, and shifting to subsequent stations.
This document discusses contouring and contour maps. It defines a contour line as a line connecting points of equal elevation. The vertical distance between consecutive contours is called the contour interval, which depends on factors like the nature of the ground and the map scale. Contour maps show the topography of an area and can be used for engineering projects, route selection, and estimating earthworks. Methods of plotting contours include direct methods using levels or hand levels, and indirect methods like gridding, cross-sectioning, and radial lines. Characteristics of contours provide information about the landscape.
Introduction, electromagnetic spectrum, electromagnetic distance measurement, types of EDM instruments, electronic digital theodolites, total station, digital levels, scanners for topographical survey, global positioning system.
Leveling is a surveying technique used to determine differences in elevation between points. It involves measuring vertical distances between a fixed benchmark and other points using a leveling instrument, leveling rod, and trigonometric leveling. There are two main methods for leveling - the height of instrument method and rise and fall method. Leveling is used to establish elevations, construct contour maps, and determine cut/fill volumes for engineering projects.
1. Levelling is used to determine relative heights and elevations of points and establish points at required elevations. It involves using instruments like levels and staffs.
2. There are different types of levels (dumpy, tilting, wye, automatic) and staffs (self-reading, target). Precise levelling is done to establish permanent benchmarks.
3. Adjustments must be made to level instruments during setup and permanently. Methods like differential, profile and cross levelling are used depending on the task. Reciprocal levelling involves backsight-foresight exchange to check for errors.
This document provides an overview of tacheometric surveying. It discusses the principles and methods of tacheometry including the stadia, fixed hair, movable hair, and tangential methods. Formulas are provided for calculating horizontal distance, vertical distance, and elevation using each method. The key principles are that tacheometry uses trigonometric relationships based on intercepts measured through a stadia diaphragm to determine horizontal and vertical distances between instrument and target stations.
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.
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.
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.
This document is a field report for a traversing survey conducted by students. It contains unadjusted and average field data from three separate traverses, including measured horizontal and vertical angles between stations. It also shows the calculations to determine angular errors, angle adjustments, course bearings, latitudes and departures, adjusted coordinates, and station positions. The objectives, equipment used, and results are presented in tables and graphs.
Tacheometric surveying is a method that determines horizontal and vertical distances optically rather than using a tape or chain. It uses a theodolite fitted with a stadia diaphragm containing hairs to rapidly measure distances. There are different systems, including the stadia system which uses fixed or movable hairs, and the tangential system. Formulas are used to calculate distances and elevations based on staff intercept readings and vertical angles observed. The constants of the instrument such as the multiplying constant and additive constant must also be determined.
Tacheometric surveying is a method of surveying that uses optical instruments to rapidly measure horizontal and vertical distances between points. It is well-suited for difficult terrain where direct measurements with tapes or chains are impossible. A tacheometer, which is a theodolite fitted with a stadia diaphragm, is used to measure the angle subtended by a known distance on a stadia rod or staff at a point. This allows the horizontal distance and elevation of points to be calculated trigonometrically without direct measurement. Common tacheometric methods include fixed hair stadia, subtense, and tangential systems. Field procedures involve establishing instrument stations along a traverse and taking angular and stadia rod readings
This document provides information on tacheometric surveying. It discusses that tacheometric surveying uses angular observations with an instrument called a tachometer to determine horizontal and vertical distances. It is used in rough terrain where direct leveling and chaining are difficult. The document outlines the various components and methods used in tacheometric surveying, including fixed hair and movable hair stadia methods, tangential and subtense bar systems, and principles of stadia measurements for both perpendicular and inclined lines of sight.
LABORATORY MANUAL FOR SURVEYING-II
AS PER DBATU's Syllabus.. all experiments and field work-related data will be helpful by this manual to all BTECH. Students belong to DBATU, Lonere
This document discusses tachymetry, which is a method of surveying that uses optical means to measure distances and heights between points. It describes the stadia method, which uses a telescope with crosshairs and a stadia rod to measure distances without a tape. The document outlines the principles, systems, and formulas used in tachymetry, including evaluating stadia constants, inclined sights with vertical and normal staff positions, and comparing the two staff holding methods. It provides an example calculation of horizontal and vertical distances using inclined sight formulas.
Introduction, purpose, principle, instruments, methods of tacheometry, stadia constants, anallatic lens, Subtense bar, field work in tacheometry, reduction of readings, errors and precisions.
Tacheometry is a surveying method that uses angular measurements from a tacheometer to determine horizontal and vertical distances. It is well-suited for hilly areas where chaining distances is difficult. The document provides procedures to determine the multiplying and additive constants of a tacheometer through stadia tacheometry. This involves setting up the instrument and measuring staff intercepts at known distances to solve equations and calculate the constants. The constants are then used in tacheometric formulas to determine horizontal distances, vertical distances, and elevations for different sighting configurations of the staff.
The document discusses different methods of surveying using a theodolite, including:
1. Tacheometry/stadia methods which use a theodolite and stadia hairs to measure horizontal and vertical distances to points by taking angle and stadia readings.
2. Trigonometric leveling which uses a total station to measure slope distance and vertical angle to determine elevation differences between points.
3. Short line leveling which uses vertical angle or zenith angle measurements between a total station and target to calculate elevation differences between points based on their heights and angles.
The document discusses angle measurement using transits, theodolites, and total stations. It provides definitions of horizontal, vertical, and zenith angles. It describes the basic components and functions of transits and theodolites, including different types like repeating theodolites. The document outlines procedures for measuring horizontal and vertical angles, including methods of repetition and reiteration. It also discusses instrumental errors and how to perform temporary and permanent adjustments of a theodolite.
This document provides details on a topographic survey of a plot of land using the radiation method. Key points:
- A topographic survey was conducted of a plot of land using a total station to measure azimuth angles and distances to boundary points.
- Calculations were shown to determine horizontal distances from inclined distances and instrument heights.
- A sketch, plan, and field book with results were included.
- The radiation method was concluded to be useful for irregularly shaped lands and calculations were important to perform correctly.
1. The document discusses various topics related to surveying including tacheometry, leveling, and triangulation. It provides definitions and explanations of terms like tacheometer, analytic lens, substance bar, and different tacheometric measurement systems.
2. Examples are given for calculating horizontal and vertical distances using tacheometric observations. The document also includes multi-part problems for determining reduced levels, horizontal distances, and elevations from tacheometric data.
3. Additional surveying concepts covered include permanent and temporary bench marks, arbitrary bench marks, extension of baselines, trigonometric leveling, axis signal corrections, and geodetic surveying. Triangulation methods and terms
This document contains the fieldwork report for a traversing survey conducted by students using a theodolite. It includes an introduction to traversing surveys, descriptions of the equipment used including a theodolite, tripod, plumb bob and ranging rods. The objectives of the fieldwork and field data collected are presented. Calculations of angular errors and adjustments, length measurements using stadia methods, and course latitude and departure are shown. A table of station coordinates and graph are included. The report discusses achieving the required accuracy and applying compass rule corrections. It is concluded that the objectives were met by obtaining necessary data to analyze and adjust errors in the closed loop traverse.
This document provides details on a fieldwork report for a traversing exercise conducted by students. It includes an introduction to traversing, descriptions of the equipment used including a theodolite, tripod, plumb bob and ranging rod. The objectives and field data from the exercise are presented. Calculations are shown for angular errors and adjustments, determining lengths using stadia measurements, and calculating latitudes, departures and station coordinates. Small errors were found and corrected using compass rule adjustments. The summary provides an acceptable level of accuracy and demonstrates the techniques learned for conducting a traversing survey.
This document describes a closed traverse survey conducted by a group of students. It includes an introduction to traversing, the equipment used (theodolite, tripod, leveling rods), field data collection methods, calculations of angular errors, distances, azimuths, latitudes and departures, and station coordinates. The group adjusted their results based on the Compass Rule correction and achieved an accuracy of 1:1088 for the closed traverse. They discussed lessons learned from conducting the fieldwork.
Tacheometry is a surveying method that uses a tacheometer, which is a telescope fitted with a stadia hair micrometer, to measure distances. There are three types of telescopes used: external focusing, internal focusing, and external focusing with an additional anallatic lens. An anallatic lens provides simpler distance calculations by making the constant (f+c) equal to 0. Essential characteristics of a tacheometer include a focal length constant of 100, an anallatic lens, high magnification, and a clear image. Distance measurements use a stadia rod or leveling staff measured in meters, decimeters, and centimeters. The fixed hair method takes readings from three hairs on the staff to determine
This document provides details of a fieldwork report for a traverse survey conducted by a group of quantity surveying students. It includes:
- Objectives of the fieldwork to enhance surveying skills and apply classroom theories.
- Description of the equipment used including a theodolite, tripod, plumb bob and level rod.
- Raw data collected at stations A, B, C and D including angles, distances and calculations.
- Adjusted data with corrected angles, bearings, latitudes and departures, and error of closure calculation showing the traverse is acceptable.
Tacheometry is a surveying method that determines horizontal distances and vertical elevations from observed vertical angles and staff intercept readings using trigonometry. It is used for topographic mapping, difficult terrain surveys, and establishing secondary control points. Tacheometry systems are either stadia, which considers staff intercepts at stadia hairs, or non-stadia, which uses telescopes without stadia and tangential or subtense bar methods. An anallactic lens in some tacheometers reduces the stadia constant to directly relate staff intercept to measured distance. Formulas are provided to calculate horizontal distance, vertical distance, and reduced level from observed angles for various line of sight inclinations and staff orientations.
An axial flow reaction turbine is one where water flows parallel to the axis of rotation and part of the pressure energy is converted to kinetic energy as it passes through the runner. The Kaplan turbine is an axial flow reaction turbine where the vanes on the hub are adjustable. It is suitable for low head applications. The main parts are the scroll casing, guide vanes, hub/runner with adjustable blades, and draft tube.
The document discusses fluids mechanics and provides information about various fluid properties and concepts. It defines fluid, states of matter, density, viscosity, surface tension, capillarity, and vapor pressure. It also discusses fluid pressure and different types of pressure measurements including manometers, mechanical gauges, and electronic gauges. Specific devices like piezometer, U-tube manometer, differential manometer, and bourdon tube pressure gauge are explained. Course outcomes related to understanding and applying concepts of fluid statics, kinematics, dynamics, and pressure measurements are also listed.
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.
Compass surveying is a technique used to measure angles and distances to determine locations and boundaries. A compass is used to determine direction while measuring distances helps establish positions relative to starting points. Together, angle and distance measurements allow surveyors to create maps and establish property lines.
The document discusses theodolite traversing and provides definitions and explanations of various parts and adjustments of a transit theodolite. It describes the purpose of a theodolite, defines key terms, and explains how to perform temporary and permanent adjustments of the instrument. Specifically, it outlines how to level the theodolite, set the verniers, and adjust the horizontal and vertical hairs to ensure the line of collimation coincides with the optical axis.
Offsets are lateral measurements taken to locate ground features in relation to survey lines. There are two main types of offsets - perpendicular offsets, which are taken at right angles to the survey line, and oblique offsets, which are taken at non-right angles. Various instruments can be used to measure and set offsets precisely, including tapes, cross staffs, optical squares, and prism squares. The 3-4-5 method can also be used to establish perpendicular offsets from a survey line using basic geometry principles.
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tacheometric surveying
1. TACHEOMETRIC SURVEYING
Tacheometry or tachemetry or telemetry is a branch of angular
surveying in which the horizontal and Vertical distances of points are
obtained by optical means as opposed to the ordinary slower process
of measurements by tape or chain.
• The method is very rapid and convenient.
• It is best adapted in obstacles such as steep and broken ground,
deep revines, stretches of water or swamp and so on, which make
chaining difficult or impossible,
• The primary object of tacheometry is the preparation of contoured
maps or plans requiring both the horizontal as well as Vertical
control. Also, on surveys of higher accuracy, it provides a check on
distances measured with the tape.
Tacheometry (from Greek, quick measure), is a system of
rapid surveying, by which the positions, both horizontal
and vertical, of points on the earth surface relatively to
one another are determined without using a chain or tape
or a separate leveling instrument.
2. Uses of Tacheometry
The tacheometric methods of surveying are used with
advantage over the direct methods of measurement of horizontal
distances and differences in elevations. Some of the uses are:
Preparation of topographic maps which require both elevations and
horizontal distances.
Survey work in difficult terrain where direct methods are
inconvenient
Detail filling
Reconnaissance surveys for highways, railways, etc.
Checking of already measured distances
Hydrographic surveys and
Establishing secondary control.
3. INSTRUMENTS
-An ordinary transit theodolite fitted with a stadia diaphragm is generally used
for tacheometric survey.
- The stadia diaphragm essentially consists of one stadia hair above and the
other an equal distance below the horizontal cross-hair, the stadia hairs being
mounted in the ring and on the same vertical plane as the horizontal and
vertical cross-hairs.
Different forms of stadia diaphragm commonly used
Stadia is a tacheometric form of distance measurement that relies on fixed
angle intercept.
4. The telescope used in stadia surveying are of three kinds:
(1) The simple external-focusing telescope
(2) the external-focusing anallactic telescope (Possor`s telescope)
(3) the internal-focusing telescope.
A tacheometer must essentially incorporate the following features:
(i) The multiplying constant should have a nominal value of 100 and the error
contained in this value should not exceed 1 in 1000.
(ii) The axial horizontal line should be exactly midway between the other two
lines.
(iii) The telescope should be truly anallactic.
(iv) The telescope should be powerful having a magnification of 20 to 30
diameters.
• The aperture of the objective should be 35 to 45 mm in diameter to have a
sufficiently bright image.
• For small distances (say upto 100 meters), ordinary levelling staff may be
used. For greater distances a stadia rod may be used.
• A stadia rod is usually of one piece, having 3 – 5 meters length.
• A stadia rod graduated in 5 mm (i.e. 0.005 m) for smaller distances and while
for longer distances, the rod may be graduated in 1 cm (i.e. 0.01 m).
6. Different systems of Tacheometric Measurement:
The various systems of tacheometric survey may be classified as
follows:
The stadia System
(a) Fixed Hair method of Stadia method
(b) Movable hair method, or Subtense method
The tangential system
Measurements by means of special instruments
The principle common to all the systems is to calculate the horizontal
distance between two points A and B and their distances in elevation, by
observing
(i) The angle at the instrument at A subtended by a known short distance
along a staff kept at B, and
(ii) the vertical angle to B from A.
7. (a) Fixed hair method
In this method, the angle at the instrument at A
subtended by a known short distance along a staff kept at
B is made with the help of a stadia diaphragm having
stadia wires at fixed or constant distance apart.
The readings are on the staff corresponding to all the
three wires taken.
The staff intercept, i.e., the difference of the readings
corresponding to top and bottom stadia wires will
therefore depend on the distance of the staff from the
instrument.
When the staff intercept is more than the length of the
staff, only half intercept is read.
For inclined sight, readings may be taken by keeping
the staff either vertical or normal to the line of sight.
This is the most common method is tacheometry and
the same ‘stadia method’ generally bears reference to this
method.
8. Subtense Method
This method is similar to the fixed hair method except that the stadia
interval is variable.
Suitable arrangement is made to vary the distance between the stadia hair
as to set them against the two targets on the staff kept at the point under
observation.
Thus, in this case, the staff intercept, i.e., the distance between the two
targets is kept fixed while the stadia interval, i.e., the distance between the
stadia hair is variable.
As in the case of fixed hair method, inclined sights may also be taken.
Tangential Method
In this method, the stadia hairs are not used, the readings being taken
against the horizontal cross-hair.
To measure the staff intercept, two pointings of the instruments are,
therefore, necessary.
This necessitates measurement of vertical angles twice for one single
observation.
9. PRINCIPLE OF STADIA METHOD
The stadia method is based on the principle that the ratio of the
perpendicular to the base is constant in similar isosceles triangles.
A
O
A2
A1
B2
B1
B
C2 C1 C
)
β
In figure, let two rays OA and OB be equally inclined to central ray OC.
Let A2B2, A1B1 and AB be the staff intercepts. Evidently,
OC2
A2B2
OC1
A1B1
OC
AB
= =
= constant k = ½ cot
β
2
This constant k entirely depends upon the magnitude of the angle β.
10. In actual practice, observations may be made with either horizontal line of
sight or with inclined line of sight.
In the later case the staff may be kept either vertically or normal to the line
of sight.
First the distance-elevation formulae for the horizontal sights should be
derived.
Horizontal Sights:
i
.
f2
f1
s
O
d
M
b
C
B
A
c
a
D
Consider the figure, in which O is the optical centre of the objective of an
external focusing telescope.
Let A, C, and B = the points cut by the three lines of sight corresponding to
three wires.
b, c, and a = top, axial and bottom hairs of the diaphragm.
ab = i = interval b/w the stadia hairs (stadia interval)
AB = s = staff intercept;
f = focal length of the objective
11. f1 = horizontal distance of the staff from the optical centre of the objective
f2 = horizontal distance of the cross-wires from O.
d = distance of the vertical axis of the instrument from O.
D = horizontal distance of the staff from the vertical axis of the instruments.
M = centre of the instrument, corresponding to the vertical axis.
Since the rays BOb and AOa pass through the optical centre, they are straight so
that AOB and aOb are similar. Hence,
f1 s
f2 i
=
Again, since f1 and f2 are conjugate focal distances, we have from lens formula,
1 1 1
f f2 f1
+=
Multiplying throughout by ff1, we get f1 = f + f
f1
f2
Substituting the values of in the above, we get
f1 s
f2 i
=
f1 = f + f
s
i
Horizontal distance between the axis and the staff is D = f1 + d
D = s + (f + d) = k . s + C
f
i
12. Above equation is known as the distance equation. In order to get the
horizontal distance, therefore, the staff intercept s is to be found by subtracting
the staff readings corresponding to the top and bottom stadia hairs.
The constant k = f/i is known as the multiplying constant or stadia interval
factor and the constant (f + d) = C is known as the additive constant of the
instrument.
Determination of constant k and C
The values of the multiplying constant k and the additive constant C can be
computed by the following methods:
1st
method:
In this method, the additive constant C = (f + d) is measured from the
instrument while the multiplying constant k is computed from field
observations:
1. Focus the instrument to a distant object and measure along the telescope
the distance between the objective and cross-hairs,
2. The distance d between the instrument axis and the objective is variable in
the case of external focusing telescope, being greater for short sights and
smaller for long sights. It should, therefore be measured for average sight.
Thus, the additive constant (f + d) is known.
1 1 1
f f1 f2
+=
13. 3. To calculate the multiplying constant k, measure a known distance D1 and
take the intercept s1 on the staff kept at that point, the line of sight being
horizontal. Using the equation,
D1 = ks1 + C or k =
For average value, staff intercepts, s2, s3 etc., can be measured
corresponding to distance D2, D3 etc., and mean value can be calculated.
Note: In case of some external focusing instruments, the eye-piece-diaphragm
unit moves during focusing. For such instruments d is constant and does not
vary while focusing.
D1 – C
s
2nd method:
In this method, both the constants are determined by field observations as
under:
1. Measure a line, about 200m long, on fairly level ground and drive pegs at
some interval, say 50 meters.
2. Keep the staff on the pegs and observe the corresponding staff intercepts
with horizontal sight.
3. Knowing the values of D and s for different points, a number of
simultaneous equations can be formed by substituting the values of D and s
in equation D = k.s + C. The simultaneous solution of successive pairs will
give the values of k and C, and the average of these can be found.
14. For example, if s1 is the staff intercept corresponding to distance D1 and s2
corresponding to D2 we have,
D1 = k.s1 + C . . . . . (i) and D2 = k. s2 + C . . . . . (ii)
Subtracting (i) from (ii), we get
k =
D2 – D1
s2 – s1
. . . . . . . . . (1)
Substituting the values of k in (i), we get
C = D1 - s1
D2 – D1
s2 – s1
=
D1s2 – D2s1
s2 – s1
. . . . . . . . . (2)
Thus equation (1) and (2) give the values of k and C.
15. Distance and Elevation formulae for Staff Vertical : Inclined SightDistance and Elevation formulae for Staff Vertical : Inclined Sight
Let P = Instrument station; Q = Staff station
M = position of instruments axis; O = Optical centre of the objective
A, C, B = Points corresponding to the readings of the three hairs
s = AB = Staff intercept; i = Stadia interval
Ө = Inclination of the line of sight from the horizontal
L = Length MC measured along the line of sight
D = MQ’ = Horizontal distance between the instrument and the staff
V = Vertical intercept at Q, between the line of sight and the horizontal line
h = height of the instrument; r = central hair reading
β = angle between the two extreme rays corresponding to stadia hairs.
16. • Draw a line A’CB’ normal to the line of sight OC.
• Angle AA`C = 900
+ β/2, being the exterior angle of the ∆COA`.
• Similarly, from ∆COB`, angle OB`C = angle BB`C = 900
– β/2.
h
B
A
O
D
P
A`
C
B`
Q
Q`
M
r
V
Ө
β
L
Ө
17. Since β/2 is very small (its value being equal to 17’ 11” for k = 100), angle AA’C
and angle BB’C may be approximately taken equal to 900
.
∟AA’C = ∟BB’C = 900
From ∆ ACA’, A’C = AC cos Ө or A’B’ = AB cos Ө = s cos Ө ……….(a)
Since the line A’B’ is perpendicular to the line of sight OC, equation D = k s + C
is directly applicable. Hence, we have
MC = L = k . A’B’ + C = k s cosӨ + C . . . . . . . (b)
The horizontal distance
D = L cosӨ = (k s cosӨ + C) cosӨ
D = k s cos2
Ө + C cosӨ . . . . . . (1)
Similarly, V = L sin Ө = (k s cosӨ + C) sinӨ = k s cosӨ . sinӨ + C sinӨ
V = k s + C sinӨ
sin2Ө
2
. . . . . . (2)
Thus equations (1) and (2) are the distance and elevation formulae for inclined line
of sight.
18. (a) Elevation of the staff station for angle of elevationElevation of the staff station for angle of elevation
If the line of sight has an angle of elevation Ө, as shown in the figure, we
have
Elevation of staff station = Elevation of instrument station + h + V – r.
(b) Elevation of the staff station for the angle of depression:
Elevation of Q = Elevation of P + h – V - r
19. Distance and Elevation formulae for Staff Normal : Inclined SightDistance and Elevation formulae for Staff Normal : Inclined Sight
h
B
A
O
D
P
C
C`
Q
Q`
M
rcosӨ
V
Ө
β
L
Ө
L cosӨ rsinӨ
Figure shows the case when the staff is held normal to the line of sight.
20. Case (a): Line of Sight at an angle of elevation Ө
Let AB = s = staff intercept;
CQ = r = axial hair reading
With the same notations as in the last case, we have
MC = L = K s + C
The horizontal distance between P and Q is given by
D = MC’ + C’Q’ = L cosӨ + r sinӨ
= (k s + C) cosӨ + r sinӨ . . . . . (3)
Similarly, V = L sinӨ = (k s + C) sinӨ . . . . . (4)
21. Case (a): Line of Sight at an angle of depression Ө
rsinӨ
M
P
h
Ө
A
C
C’
Q
Q’
B
C1
D
L cosӨ
rcosӨ
V
O
Figure shows the line of sight depressed downwards,
MC = L = k s + C
D = MQ’ = MC’ – Q’C’
= L cosӨ - r sinӨ
D = (k s + C) cosӨ - r sinӨ . . . . . (5)
V = L sinӨ = (k s + C) sinӨ
. . . . . (6)
Elevation of Q = Elevation of P + h – V – r cosӨ