This document describes methods of trigonometric leveling to determine the elevation of points. It discusses using a theodolite to measure vertical angles and calculate heights based on trigonometric functions. The key methods covered are:
1. Direct and reciprocal methods of observation between two stations to eliminate corrections.
2. Determining heights when the base is accessible or inaccessible using one or two instrument stations, applying corrections for curvature and refraction based on distance.
3. Calculating heights when instrument stations are at different elevations, providing equations to solve for distance and elevation.
This document discusses several types of setting out works including:
1. Setting out a foundation plan using a center line plan and batter boards. Batter boards are used to accurately transfer the center line onto the work site.
2. Setting out a sewer line by fixing stakes along the proposed center line and excavating the trench to the desired width and depth. Cross heads and sight rails are also used to maintain proper gradient and alignment.
3. Setting out a culvert involves marking points along the center lines X1 and Y1 based on given distances from the origin point O. Pegs are placed at the intersection of the points using two tapes held at equal distances between assistants. The culvert is then set
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.
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
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
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 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.
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.
This document discusses several types of setting out works including:
1. Setting out a foundation plan using a center line plan and batter boards. Batter boards are used to accurately transfer the center line onto the work site.
2. Setting out a sewer line by fixing stakes along the proposed center line and excavating the trench to the desired width and depth. Cross heads and sight rails are also used to maintain proper gradient and alignment.
3. Setting out a culvert involves marking points along the center lines X1 and Y1 based on given distances from the origin point O. Pegs are placed at the intersection of the points using two tapes held at equal distances between assistants. The culvert is then set
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.
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
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
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 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.
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.
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.
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 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.
Surveying is an important part of Civil engineering. Various part like theodolite, plane table surveying, computation of area and volume are useful for all university examination and other competitive examination
The theodolite is an instrument used to measure horizontal and vertical angles that is more precise than a magnetic compass. It can measure angles to an accuracy of 10-20 seconds whereas a compass is only accurate to 30 minutes. The theodolite is used to measure horizontal and vertical angles when objects are at a distance or elevation where more precise measurements are needed. The method of surveying that uses a theodolite to measure angles is called theodolite surveying. The theodolite can be used to measure angles, bearings, distances, elevations, set out curves, and for mapping and construction applications.
Electronic Distance Measurement (EDM) uses electromagnetic waves like light or radio waves to measure distances. EDM instruments transmit a signal that bounces off a reflecting prism and returns to the instrument. The distance is calculated based on the time it takes for the signal to return. EDM has largely replaced tape measurements and improved surveying efficiency. Modern EDM instruments are integrated into total stations and can measure slope distances with millimeter accuracy over several kilometers.
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.
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.
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.
This document provides an overview of surveying and leveling. It defines surveying as determining the relative positions of points on Earth through direct or indirect measurements. The main objectives of surveying are preparing maps and plans. Leveling is defined as determining relative heights or elevations of points through direct measurement of vertical distances from a reference level. Common instruments used for leveling include a level, tripod, staff, tape, and pegs. Leveling follows the principle of obtaining a horizontal line of sight to measure vertical distances of points above or below this line. Key leveling terms defined include bench mark, height of instrument, backsight, foresight, and change point. Methods for recording level data in a field book are also
This document discusses trigonometric levelling, which is a method of determining elevation differences between stations using vertical angles and known distances. It presents three cases for determining the elevation of a point using a theodolite: 1) when the base of the object is accessible, 2) when the base is inaccessible and instrument stations are in the same vertical plane, and 3) when the base is inaccessible and instrument stations are not in the same vertical plane. Equations for calculating relative heights are provided for each case using trigonometric functions of the vertical angles and distances between points. Corrections may be needed for long distances to account for earth's curvature and refraction.
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 discusses control surveying and triangulation. It notes that control surveying must account for the curvature of the Earth and refraction, as lines of sight are not entirely straight. It distinguishes between plane and geodetic surveying, with the latter accounting for the spherical shape of the Earth. The document then discusses establishing control points through triangulation, including different classes of triangulation, steps in triangulation like selecting stations, and erecting signals and towers.
This document provides an overview of surveying and leveling. It defines surveying as determining the relative positions of points on earth through direct or indirect measurements. Leveling is a branch of surveying that finds elevations of points with respect to a datum. There are various types of surveys classified by nature, object, or instruments used. Linear measurements can be direct via chaining or indirect using optical/electronic methods. Ranging is used to establish intermediate points when a survey line exceeds the chain length.
Theodolite traversing, purpose and principles of theodolite traversingDolat Ram
ย
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
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 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.
1. The document describes a civil engineering experiment to collect elevation data along a highway through profile leveling and cross-section leveling. Profile leveling provided centerline elevation readings at 20m intervals, while cross-section leveling obtained side elevations at one station.
2. The data collected included station positions, backsight, intermediate, and foresight elevation readings. This was used to plot the profile diagram showing the sloping road elevation, and cross-section diagram showing the center higher than the sides.
3. The conclusion was that the experiment successfully collected the required elevation data to analyze the road profile and cross-section, finding the centerline sloped down and was higher than both road sides at the
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.
This document describes the method of indirect leveling using a theodolite to determine relative heights of points. There are three cases: [1] when the base of the object is accessible, [2] when the base is inaccessible but the instrument stations and object are in the same vertical plane, and [3] when the base is inaccessible and stations/object are not in the same plane. Corrections must be applied for earth's curvature and refraction over long distances. The reciprocal method can be used to eliminate these corrections. Equations are provided to calculate elevations of points for each case.
Plane and Applied Surveying 2
Trigonometric Levelling theory
-What is Trigonometric Levelling.
-Measurement Using Trigonometry.
Measurement Using Trigonometry.
-The vertical angle and the slope distance between the two points are measured.
-If You Are Able To Get to the base of the Tower Or The Building.
Trigonometric Levelling
I- If base of the object is accessible:
1. Instrument at station A is lower than station B.
The three points (A, B, and O) are on the same vertical plane
2 Instrument at point B is lower than A.
The three points (A, B, and O) are on the same vertical plane.
3. If the two instrument heights were at the same level.
*Example:
Find the vertical height of electrical column over a hill. The reading is taken from two
instrument station (P, and R), and the horizontal distance between thereof is (60 m). The
horizontal angle of RPQ = 60ยฐ30โฒ
, and the horizontal angle of PRQ = 68ยฐ18โฒ
. The vertical
angle from P to Q =10ยฐ12โฒ
, and the vertical angle from R to Q = 10ยฐ48โฒ
.
Find the reduced level of point Q if the reduced level of (B.M) = 435.065m and the staff
reading from P and Rare (1.965, and 2.055) m respectively. And then check the result.
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
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.
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 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.
Surveying is an important part of Civil engineering. Various part like theodolite, plane table surveying, computation of area and volume are useful for all university examination and other competitive examination
The theodolite is an instrument used to measure horizontal and vertical angles that is more precise than a magnetic compass. It can measure angles to an accuracy of 10-20 seconds whereas a compass is only accurate to 30 minutes. The theodolite is used to measure horizontal and vertical angles when objects are at a distance or elevation where more precise measurements are needed. The method of surveying that uses a theodolite to measure angles is called theodolite surveying. The theodolite can be used to measure angles, bearings, distances, elevations, set out curves, and for mapping and construction applications.
Electronic Distance Measurement (EDM) uses electromagnetic waves like light or radio waves to measure distances. EDM instruments transmit a signal that bounces off a reflecting prism and returns to the instrument. The distance is calculated based on the time it takes for the signal to return. EDM has largely replaced tape measurements and improved surveying efficiency. Modern EDM instruments are integrated into total stations and can measure slope distances with millimeter accuracy over several kilometers.
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.
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.
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.
This document provides an overview of surveying and leveling. It defines surveying as determining the relative positions of points on Earth through direct or indirect measurements. The main objectives of surveying are preparing maps and plans. Leveling is defined as determining relative heights or elevations of points through direct measurement of vertical distances from a reference level. Common instruments used for leveling include a level, tripod, staff, tape, and pegs. Leveling follows the principle of obtaining a horizontal line of sight to measure vertical distances of points above or below this line. Key leveling terms defined include bench mark, height of instrument, backsight, foresight, and change point. Methods for recording level data in a field book are also
This document discusses trigonometric levelling, which is a method of determining elevation differences between stations using vertical angles and known distances. It presents three cases for determining the elevation of a point using a theodolite: 1) when the base of the object is accessible, 2) when the base is inaccessible and instrument stations are in the same vertical plane, and 3) when the base is inaccessible and instrument stations are not in the same vertical plane. Equations for calculating relative heights are provided for each case using trigonometric functions of the vertical angles and distances between points. Corrections may be needed for long distances to account for earth's curvature and refraction.
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 discusses control surveying and triangulation. It notes that control surveying must account for the curvature of the Earth and refraction, as lines of sight are not entirely straight. It distinguishes between plane and geodetic surveying, with the latter accounting for the spherical shape of the Earth. The document then discusses establishing control points through triangulation, including different classes of triangulation, steps in triangulation like selecting stations, and erecting signals and towers.
This document provides an overview of surveying and leveling. It defines surveying as determining the relative positions of points on earth through direct or indirect measurements. Leveling is a branch of surveying that finds elevations of points with respect to a datum. There are various types of surveys classified by nature, object, or instruments used. Linear measurements can be direct via chaining or indirect using optical/electronic methods. Ranging is used to establish intermediate points when a survey line exceeds the chain length.
Theodolite traversing, purpose and principles of theodolite traversingDolat Ram
ย
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
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 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.
1. The document describes a civil engineering experiment to collect elevation data along a highway through profile leveling and cross-section leveling. Profile leveling provided centerline elevation readings at 20m intervals, while cross-section leveling obtained side elevations at one station.
2. The data collected included station positions, backsight, intermediate, and foresight elevation readings. This was used to plot the profile diagram showing the sloping road elevation, and cross-section diagram showing the center higher than the sides.
3. The conclusion was that the experiment successfully collected the required elevation data to analyze the road profile and cross-section, finding the centerline sloped down and was higher than both road sides at the
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.
This document describes the method of indirect leveling using a theodolite to determine relative heights of points. There are three cases: [1] when the base of the object is accessible, [2] when the base is inaccessible but the instrument stations and object are in the same vertical plane, and [3] when the base is inaccessible and stations/object are not in the same plane. Corrections must be applied for earth's curvature and refraction over long distances. The reciprocal method can be used to eliminate these corrections. Equations are provided to calculate elevations of points for each case.
Plane and Applied Surveying 2
Trigonometric Levelling theory
-What is Trigonometric Levelling.
-Measurement Using Trigonometry.
Measurement Using Trigonometry.
-The vertical angle and the slope distance between the two points are measured.
-If You Are Able To Get to the base of the Tower Or The Building.
Trigonometric Levelling
I- If base of the object is accessible:
1. Instrument at station A is lower than station B.
The three points (A, B, and O) are on the same vertical plane
2 Instrument at point B is lower than A.
The three points (A, B, and O) are on the same vertical plane.
3. If the two instrument heights were at the same level.
*Example:
Find the vertical height of electrical column over a hill. The reading is taken from two
instrument station (P, and R), and the horizontal distance between thereof is (60 m). The
horizontal angle of RPQ = 60ยฐ30โฒ
, and the horizontal angle of PRQ = 68ยฐ18โฒ
. The vertical
angle from P to Q =10ยฐ12โฒ
, and the vertical angle from R to Q = 10ยฐ48โฒ
.
Find the reduced level of point Q if the reduced level of (B.M) = 435.065m and the staff
reading from P and Rare (1.965, and 2.055) m respectively. And then check the result.
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
This is based on the surveying branch.. which shows 3 cases here.. for civil engineering students .. and as well as also who want to know about what is Trigonometric leveling..
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.
Trigonometric leveling is used to determine elevation differences between stations using vertical angles and known distances measured by a theodolite. There are three cases for determining the elevation of a point: 1) when the base is accessible, the elevation is calculated as the distance times the tangent of the vertical angle; 2) when the base is inaccessible but stations are in the same vertical plane, equations relate the elevations using tangents of vertical angles; 3) when the base is inaccessible and stations are not in the same plane, sine rule is used to calculate distances and elevations are found using tangents of vertical angles. Corrections may be needed for earth curvature and refraction over long distances.
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
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.
Introduction, purpose, principle, instruments, methods of tacheometry, stadia constants, anallatic lens, Subtense bar, field work in tacheometry, reduction of readings, errors and precisions.
This document discusses triangulation survey methods. Triangulation uses a network of triangles to determine coordinate positions of survey points. It is preferred for hilly areas where stations can be clearly visible from each other. The key steps are:
1) Establishing a baseline between two points with known coordinates
2) Measuring horizontal angles at stations to other points
3) Using trigonometry to calculate lengths of triangle sides and coordinate positions of additional points
4) Adjusting measurements and computations to minimize errors
Triangulation provides control points for detailed surveys and is suitable for engineering projects over large areas. Resection and intersection methods are discussed to compute point positions from angle and distance measurements.
Triangulation is a surveying method that uses triangles to determine locations of points. It involves establishing a network of triangles connecting known points, then measuring angles and lengths within the triangles. Key steps include selecting station locations with good intervisibility, measuring baselines and angles, computing lengths and positions using trigonometry, and establishing additional points through intersection or resection. Modern trilateration uses distance measurements instead of angles to speed up the process and improve accuracy when using electronic distance measurement.
The document describes a site surveying fieldwork involving a closed loop traverse using a theodolite. Key steps included setting up the instrument and marking stations A, B, C and D. Field angles were measured between stations and used to calculate distances, azimuths, latitudes and departures. The total angular error was distributed and corrections applied to adjusted values. Station coordinates were then computed, with the traverse closing within the acceptable accuracy range for land surveying of 1:300. The purpose was to gain practical experience in traversing techniques.
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.
1. The document discusses relief displacement in aerial photographs. Relief displacement is the displacement of an image due to variations in the terrain's relief or height.
2. It provides a derivation of the relief displacement formula: Relief Displacement = (radial distance of top point) x (height of object) / (altitude of airplane).
3. Several examples are provided to demonstrate how to use the formula to calculate relief displacement and height values given information from an aerial photograph.
Fractal dimensions of 2d quantum gravityTimothy Budd
ย
After introducing 2d quantum gravity, both in its discretized form in
terms of random triangulations and its continuum description as
Quantum Liouville theory, I will give a (non-exhaustive) review of the
current understanding of its fractal dimensions. In particular, I will
discuss recent analytic and numerical results relating to the
Hausdorff dimension and spectral dimension of 2d gravity coupled to
conformal matter fields.
The document describes procedures for measuring the height of an inaccessible building using a theodolite. It outlines 3 cases: 1) the building base is accessible, 2) the base is inaccessible but 3 points lie on the same vertical plane, and 3) the base is inaccessible and points do not lie on the same plane. For each case, it provides step-by-step instructions, formulas used, and an example field note table. Calculations involve using trigonometric functions like tangent and sine based on measured angles and distances to calculate heights.
This document summarizes different methods for setting out simple circular curves based on the instruments used. The two main methods are the linear method, which uses only a tape or chain and does not require angle measurement, and the angular method, which is used for larger curves and does involve angle measurement. Specific 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 covered are Rankine's method of tangential angles, the two theodolite method, and the tacheometric method.
This document contains a lecture outline on trigonometric leveling with examples of numerical problems. It includes:
- An introduction to trigonometric leveling and the lecturer's contact information.
- Four example problems demonstrating calculations for corrected vertical angles, central angles, curvature and refraction corrections, and determining height differences or reduced levels between stations using trigonometric leveling methods and accounting for instrument heights, signal heights, and refraction.
surveying_module-3-trigonometric-leveling by Denis Jangeed.pdfDenish Jangid
ย
surveying_module-3-Trigonometric leveling by Denis Jangeed
Methods of Observation
Method of determining the elevation of
To obtain R.L of top of a ten storeyed building
following observation were taken.
Indirect levelling on a rough
terrain
a point by theodolite
โข There are main three cases to determine the
R.L of any point.
โข Case : 1 :- Base of Object accessible.
โข Case : 2 :- Base of object inaccessible,
instrument station in the vertical plane as the
elevated object.
โข Case : 3 :- Base of the object inaccessible ,
instrument stations not in the same vertical
plane as the elevated object.
There may be two case
A. Instrument axis at same level
B. Instrument axis at different level
Angle of elevation
Height of the instrument
Calculate reduce level of the top of the tower
from the following data.
Indirect levelling on a steep slope
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.
Two way slabs are slabs that are supported on all four edges and have a ratio of less than 2 between their long and short spans. This causes them to bend in both directions. There are two types: simply supported and restrained. Simply supported slabs have corners that lift up under loading while restrained slabs have corners that are held down, producing torsion. Reinforcement is provided differently depending on the type of slab.
This document discusses one way slabs. It defines one way slabs as slabs supported by beams on two opposite sides, with the load transferred to the two supports. For a slab to be considered one way, the ratio of its long side (ly) to short side (lx) must be greater than or equal to 2. Reinforcement in a one way slab is provided only along the short span direction. In contrast, two way slabs have reinforcement in both directions since for them ly/lx is less than 2. Other types of slabs discussed include flat slabs supported directly on columns and grid slabs supported within a column-free area by perimeter beams.
The document discusses different types of columns based on bracing, length, and reinforcement. It describes braced and unbraced columns, long and short columns, and tied, spiral, and composite columns. Requirements for minimum reinforcement, lateral ties, and selection of column size are also summarized.
This document discusses development length and lap length in structural design. It defines development length as the length of reinforcement embedded in concrete required to develop the bond stress. A formula for calculating development length is provided based on bar diameter, steel stress, and design bond stress in concrete. Design bond stress values for different concrete grades are also given. Lap length refers to the overlapping length of bars and must be equal to or greater than the development length or 24 times the bar diameter, whichever is greater.
This document provides information on the analysis of T-beams, including:
1) It defines T-beams and L-beams as beams with flanges projecting from one or both sides of the web, forming a T or inverted L shape.
2) It explains the concept of a T-beam as a combination of a rectangular beam and slab portion, and provides the formula to calculate the overall depth.
3) It shows the stress-strain diagram for a T-beam and defines terms like neutral axis, compression and tension forces, and lever arms.
4) It describes how to determine the position of the neutral axis based on the relative magnitudes of compression and tension forces.
This document provides information on doubly reinforced concrete beams. It introduces the concept of doubly reinforced beams, which have reinforcement in both the tension and compression zones. This allows for an increased moment of resistance compared to singly reinforced beams. The key advantages of doubly reinforced beams are that they can be used when the applied moment exceeds the capacity of a singly reinforced beam, when beam depth cannot be increased, or when reversal of stresses may occur. The document includes stress diagrams, design concepts, and differences between singly and doubly reinforced beams.
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.
This document discusses stress diagrams and design considerations for singly reinforced concrete beams. It covers notation, stress conditions, types of failure, and formulas for moment of resistance. The key points are:
1) A stress diagram shows the compression and tension zones of a beam based on the depth of the neutral axis. The moment of resistance depends on the neutral axis location.
2) Beam sections can be balanced, under-reinforced, or over-reinforced depending on when concrete or steel yields. Under-reinforced sections are preferred.
3) Formulas are provided to calculate the moment of resistance based on the steel or concrete stresses for different section types. Reinforcement criteria specify minimum and maximum steel ratios.
This is an overview of my current metallic design and engineering knowledge base built up over my professional career and two MSc degrees : - MSc in Advanced Manufacturing Technology University of Portsmouth graduated 1st May 1998, and MSc in Aircraft Engineering Cranfield University graduated 8th June 2007.
An In-Depth Exploration of Natural Language Processing: Evolution, Applicatio...DharmaBanothu
ย
Natural language processing (NLP) has
recently garnered significant interest for the
computational representation and analysis of human
language. Its applications span multiple domains such
as machine translation, email spam detection,
information extraction, summarization, healthcare,
and question answering. This paper first delineates
four phases by examining various levels of NLP and
components of Natural Language Generation,
followed by a review of the history and progression of
NLP. Subsequently, we delve into the current state of
the art by presenting diverse NLP applications,
contemporary trends, and challenges. Finally, we
discuss some available datasets, models, and
evaluation metrics in NLP.
Covid Management System Project Report.pdfKamal Acharya
ย
CoVID-19 sprang up in Wuhan China in November 2019 and was declared a pandemic by the in January 2020 World Health Organization (WHO). Like the Spanish flu of 1918 that claimed millions of lives, the COVID-19 has caused the demise of thousands with China, Italy, Spain, USA and India having the highest statistics on infection and mortality rates. Regardless of existing sophisticated technologies and medical science, the spread has continued to surge high. With this COVID-19 Management System, organizations can respond virtually to the COVID-19 pandemic and protect, educate and care for citizens in the community in a quick and effective manner. This comprehensive solution not only helps in containing the virus but also proactively empowers both citizens and care providers to minimize the spread of the virus through targeted strategies and education.
Sachpazis_Consolidation Settlement Calculation Program-The Python Code and th...Dr.Costas Sachpazis
ย
Consolidation Settlement Calculation Program-The Python Code
By Professor Dr. Costas Sachpazis, Civil Engineer & Geologist
This program calculates the consolidation settlement for a foundation based on soil layer properties and foundation data. It allows users to input multiple soil layers and foundation characteristics to determine the total settlement.
Better Builder Magazine brings together premium product manufactures and leading builders to create better differentiated homes and buildings that use less energy, save water and reduce our impact on the environment. The magazine is published four times a year.
This is an overview of my career in Aircraft Design and Structures, which I am still trying to post on LinkedIn. Includes my BAE Systems Structural Test roles/ my BAE Systems key design roles and my current work on academic projects.
1. TRIGONOMETRIC LEVELING
Mahatma Gandhi Institute Of
Technical Education
& Research Centre, Navsari (396450)
SURVEYING
4TH SEMESTER
CIVIL ENGINEERING
PREPARED BY:
Asst. Prof. GAURANG PRAJAPATI
CIVIL DEPARTMENT
2. INTRODUCTION
โTrigonometric levelling is the process of determining the differences of elevations of
stations from observed vertical angles and known distances.โ
โข The vertical angles are measured by means of theodolite.
โข The horizontal distances by instrument
โข Relative heights are calculated using trigonometric functions.
โขIf the distance between instrument station and object is small, correction for earth's
curvature and refraction is not required.
โข If the distance between instrument station and object is large, the combined correction =
0.0673 D2 for earth's curvature and refraction is required. Where D = distance in KM.
โขIf the vertical angle is (+ve), the correction is taken as (+ve) & If the vertical angle is (-ve),
the correction is taken as (-ve)
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3. Method of Observation
โข There are two methods of observation:
1. Direct Method
2. Reciprocal method
1. Direct Method:
โข This method is useful Where is not possible to set the instrument over the station
whose elevation is to be determined. i.e. To determine height of a tower.
โข In this method, the instrument is set on the station on the ground whose elevation is
known. And the observation of the top of the tower is taken.
โข Sometimes, the instrument is set on any suitable station and the height of instrument
axis is determined by taking back sight on B.M.
โข Then the observation of the top of the tower is taken.
โข In this method, the instrument can not be set on the top of the tower and observation
can not be taken of the point on the ground.
โข If the distance between instrument station and object is large, the combined
correction = 0.0673 D2 for earth's curvature and refraction is required. Where D =
distance in KM.
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4. Method of Observation
2. Reciprocal method:
โข In this method, the instrument is set on each of the two stations, alternatively and
observations are taken.
โข Let, Difference in elevation between two stations A & B is to be determined.
โข First, set the instrument on A and take observation of B. Then set the instrument at
B and take observation of A.
โข Set the theodolite on A and measure the angle of elevation of B as L BAC = ฮฑ
โข Set the theodolite on B and measure the angle of depression of A as L ABCโ = ฮฒ
โข Measure the horizontal distance between A & B as D using tape.
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6. Method of Observation
โข If Distance between
A & B is Small,
AB' = AC = D
L ACB = 900
Similarly,
BA' = BC' = D
L AC'B = 900
BC = D tan ฮฑ
AC' = D tan ฮฒ
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7. Method of Observation
โข If Distance between A & B is large,
โข The correction for earth's curvature and refraction is required.
โข Combined correction = 0.0673 D2, Where D = distance in KM.
โข The difference in elevation between A & B,
H=BB'
=BC + CB'
=D tan ฮฑ + 0.0673 D2. ....(1)
โข If the angle of Depression B to A is measured,
AC'=D tan ฮฒ [ BC'= D ]
โข True difference in elevation between A & B,
H=AA'
= ACโ โ AโCโ
=D tan ฮฒ - 0.0673 D2 ....(2)
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8. Method of Observation
โข Adding equation (1) & (2),
2 H = D tan ฮฑ + D tan ฮฒ
H = D/2 [tan ฮฑ + D tan ฮฒ] ..... (3)
โข From equation (3), it can be seen that by reciprocal method of observation, the
correction for earthโs curvature and refraction can be eliminated.
R.L of station B = R.L. of station A + H
= R.L. of station A + D/2 [tan ฮฑ + D tan ฮฒ]
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9. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
โข In order to calculate the R.L. Of object, we may consider the following cases.
Case 1: Base of the object accessible
Case 2: Base of the object inaccessible, Instrument stations in the vertical plane as the
elevated object.
Case 3: Base of the object inaccessible, Instrument stations not in the same vertical
plane as the elevated object.
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10. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
Case 1: Base of the object accessible:
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11. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
A = Instrument station
B = Point to be observed
h = Elevation of B from the instrument axis
D = Horizontal distance between A and the base of object
h1 = Height of instrument (H. I.)
Bs = Reading of staff kept on B.M.
ฮฑ = Angle of elevation = L BAC
From fig.,
h = D tan ฮฑ . ....(1)
R.L. of B = R.L. of B.M. + Bs + h
= R.L. of B.M. + Bs + D. tan ฮฑ . ....(2)
โข Now, when the distance between instrument station and object is large, then
correction for earth's curvature and refraction is required.
โข combined correction = 0.0673 D2 Where D = distance in KM.
R.L. of B = R.L. of B.M. + Bs + D. tan ฮฑ + 0.0673 D2
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12. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
Case 2: Base of the object inaccessible, Instrument stations in the vertical plane as the
elevated object:
โข This method is used When it is not possible to measure the horizontal; distance (D)
between the instrument station and the base of the object.
โข In this method, the instrument is set on the two different stations and the observations
of the object are taken.
โข There may be two cases:
1. Instrument axes at the same level
2. Instrument axes at different levels
A. Height of instrument axis never to the object is lower
B. Height of instrument axis to the object is higher
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13. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
1. Instrument axes at the same level:
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14. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
A, B = Instrument station
h = Elevation of top of the object (P) from the instrument axis
b = Horizontal distance between A & B
D = Horizontal distance between A and the base of the object
ฮฑ1 = Angle of elevation from A to P
ฮฑ2 = Angle of elevation from B to P
From, ฮ PAโPโ , h1 = D tan ฮฑ1
. ....(1)
ฮ PBโPโ, h2 = (b + D) tan ฮฑ2 ....(2)
โข Equating (1) & (2),
D tan ฮฑ1 = (b + D) tan ฮฑ2
D tan ฮฑ1 = b tan ฮฑ2 + D tan ฮฑ2
D (tan ฮฑ1 - tan ฮฑ2 ) = = b tan ฮฑ2
D =
๐ ๐๐๐ ๐ถ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
....(3)
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15. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
Substitute value of D in equation (1),
D =
๐ ๐ญ๐๐ง ๐ ๐ ๐ญ๐๐ง ๐ ๐
๐ญ๐๐ง ๐ ๐โ ๐ญ๐๐ง ๐ ๐
....(4)
R.L. OF P = R.L. Of B.M. + Bs + h
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16. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
2. Instrument axes at different levels:
โข In the field, it is very difficult to keep the same height of instrument axis, at
different stations.
โข Therefore, the instrument is set at two different stations and the height of
instrument axis in both the cases is determined by taking back sight on B.M.
โข There are two cases:
A. Height of instrument axis never to the object is lower
B. Height of instrument axis to the object is higher
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17. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
A. Height of instrument axis never to the object is lower:
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18. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
From, ฮ PAโPโ , h1 = D tan ฮฑ1
. ....(1)
ฮ PBโPโโ, h2 = (b + D) tan ฮฑ2 ....(2)
Deducting equation (2) from equation (1)
h1 โ h2 = D tan ฮฑ1 - (b + D) tan ฮฑ2
= D tan ฮฑ1 - b tan ฮฑ2 โ D tan ฮฑ2
hd = D (tan ฮฑ1 - tan ฮฑ2 ) โb tan ฮฑ2 (hd = h1 - h2 )
hd + b tan ฮฑ2 = D (tan ฮฑ1 - tan ฮฑ2 )
D =
๐ก ๐+ ๐ ๐ญ๐๐ง ๐ ๐
๐ญ๐๐ง ๐ ๐โ ๐ญ๐๐ง ๐ ๐
D =
(๐ + ๐ก ๐ ๐๐จ๐ญ ๐ ๐) ๐ญ๐๐ง ๐ ๐
๐ญ๐๐ง ๐ ๐โ ๐ญ๐๐ง ๐ ๐
...(3)
Substitute value of D in equation (1),
h1 = D tan ฮฑ1
h1 =
(๐โ ๐ ๐ ๐๐๐ ๐ถ ๐) ๐๐๐ ๐ถ ๐ ๐๐๐ ๐ถ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
...(4)
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19. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
B. Height of instrument axis to the object is higher:
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20. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
From, ฮ PAโPโ , h1 = D tan ฮฑ1
. ....(1)
ฮ PBโPโโ, h2 = (b + D) tan ฮฑ2 ....(2)
Deducting equation (1) from equation (2)
h2 โ h1 = (b + D) tan ฮฑ2 - D tan ฮฑ1
= b tan ฮฑ2 + D tan ฮฑ2 โ D tan ฮฑ1
hd = b tan ฮฑ2 + D (tan ฮฑ2 - tan ฮฑ1) (hd = h1 - h2 )
hd - b tan ฮฑ2 = D (tan ฮฑ2 - tan ฮฑ1)
- hd + b tan ฮฑ2 = D (tan ฮฑ1 - tan ฮฑ2)
D =
๐ ๐๐๐ ๐ถ ๐โ๐ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
D =
(๐โ ๐ ๐ ๐๐๐ ๐ถ ๐) ๐๐๐ ๐ถ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
...(3)
Substitute value of D in equation (1),
h1 = D tan ฮฑ1
h1 =
(๐โ ๐ ๐ ๐๐๐ ๐ถ ๐) ๐๐๐ ๐ถ ๐ ๐๐๐ ๐ถ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
...(4)
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21. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
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In above two cases, the equations of D and h1 are,
D =
(๐ยฑ ๐ ๐ ๐๐๐ ๐ถ ๐) ๐๐๐ ๐ถ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
h1 =
(๐ยฑ ๐ ๐ ๐๐๐ ๐ถ ๐) ๐๐๐ ๐ถ ๐ ๐๐๐ ๐ถ ๐
๐๐๐ ๐ถ ๐โ ๐๐๐ ๐ถ ๐
Use (+) sign if A is lower & Use (-) sign if A is higher.
22. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
Case 3: Base of the object inaccessible, Instrument stations not in the same vertical
plane as the elevated object:
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23. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
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Let A and B be the two instrument stations not in the same vertical plane as that of P.
Procedure:
โข Select two survey stations A and B on the level ground and measure b as the horizontal
distance between them.
โข Set the instrument at A and level it accurately. Set the vertical Vernier to 0 degree. Bring
the altitude level bubble at the center and take a back sight hs on the staff kept at B.M.
โข Measure the angle of elevation ฮฑ1 to P.
โข Measure the horizontal angle at A, L BAC = ฮธ
โข Shift the instrument to B and Measure the angle of elevation ฮฑ2 to P.
โข Measure the horizontal angle at B as ฮฑ.
24. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
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ฮฑ1 = angle of elevation from A to P
ฮฑ2 = angle of elevation from B to P
ฮ = Horizontal angle L BAC at station A (clockwise)
ฮฑ = Horizontal angle L CBA at station B (clockwise)
B = Horizontal distance between A & B
h1= PP1= Height of object P from instrument axis of A
h2= PP2= Height of object P from instrument axis of B
In ฮ ABC, L BAC = ฮ
L ABC = ฮฑ
So, L ACB = 180 โ (ฮ + ฮฑ)
AB = b
25. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
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We know, three angles and one side of ฮ ABC. Therefore using Sine Rule, we can calculate distance AC & BC
as below.
BC =
๐ ๐๐๐ ๐ฝ
๐ฌ๐ข๐ง [๐๐๐โ ๐ฝ+๐ ]
โฆโฆ(1)
Ac =
๐ ๐๐๐ ๐ถ
๐ฌ๐ข๐ง [๐๐๐โ ๐ฝ+๐ ]
โฆโฆ(2)
Now, h1= AC tan ฮฑ1 & h2= BC tan ฮฑ2
Values of AC & BC are obtained from equation (1) & (2) as above.
R.L. of P = Height of instrument axis at A + h1 OR R.L. of P = Height of instrument axis at B + h2
Height of instrument axis at A,
= R.L. of B.M. + B.S.
= R.L. of B.M. + hs
Height of instrument axis at B = R.L. of B.M. + B.S.
26. INDIRECT LEVELLING ON A ROUGH TERRAIN
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On a rough terrain, indirect levelling can be used to determine the difference of
elevations of two point which are quite apart.
Let difference of elevation of two points P and Q is required.
27. INDIRECT LEVELLING ON A ROUGH TERRAIN
TRIGONOMETRIC LEVELING
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โข Set up the theodolite at some convenient point O1 midway between P and Q.
โข Measure the vertical angle ฮฑ1 to the station P. Also measure the horizontal distance
D1 between O1 and P.
โข Similarly, measure the vertical angle ฮฒ1 to the station Q. also measure the
horizontal distance D2 between O1 and Q.
โข Determine the difference in elevation H1 between P and Q as explained below.
โข Let us assume that,
ฮฑ1 = angle of depression
ฮฒ1 = angle of elevation
H1 = PPโ +QQโ
= (PPโ โ PโPโ) + (QQโ + QโQโ)
= (D1 tan ฮฑ1 - C1) + (C2 + D2 tan ฮฒ1) โฆ โฆ โฆ (1)
โข Where C1 and C2 are the corrections due to curvature of earth and refraction.
28. INDIRECT LEVELLING ON A ROUGH TERRAIN
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โข As the distances D1 and D2 are nearly equal, the corrections C1 and C2 are also approximately
equal.
โด H1 = D1 tan ฮฑ1 + D2 tan ฮฒ1 โฆ โฆ โฆ (2)
โข Now shift the instrument to the station O2 midway between Q and R.
โข Measure the vertical angles ฮฑ2 and ฮฒ2 to the stations Q and R and respective
horizontal distance D3 and D4.
โด Difference of elevations between Q and R is,
H2 = D3 tan ฮฑ2 + D4 tan ฮฒ2 โฆ โฆ โฆ (3)
โข Repeat the above process at the station O3
โด H3 = D5 tan ฮฑ3 + D6 tan ฮฒ3 โฆ โฆ โฆ (4)
โข Determine the difference in elevations of P and S as,
H = H1 + H2 + H3
โข โดR.L. of S = R.L. of P + H
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โข Indirect levelling is not as accurate as direct levelling with a levelling instrument. The
method is used in rough country.
โข If back sight and foresight distances are approximately equal, the effect of curvature and
refraction is eliminated.
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โข If the ground is quite steep, the method of indirect levelling can be used with
advantage.
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โข The following procedure can be used to determine the difference of elevations between P
and R.
โข Set up the instrument at a convenient station O1 on the line PR.
โข Make the line of collimation roughly parallel to the slope of the ground. Clamp the
telescope.
โข Take a back sight PPโ on the staff held at P. Also measure the vertical angle ฮฑ1 to Pโ.
Determine R.L. of Pโ as.
R.L. of Pโ = R.L. of P + PPโ
โข Take a foresight QQโ on the staff held at the turning point Q. without changing the vertical
angle ฮฑ1. Measure the slope distance PQ between P and Q.
R.L. of Q = R.L. of Pโ + PQ sin ฮฑ1 โ QQโ
OR
R.L. of Q = R.L. of P + PPโ + PQ sin ฮฑ1 โ QQโ
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โข Shift the instrument to the station O2 midway between Q and R. Make the line of
collimation roughly parallel to the slope of the grounds. Clamp the telescope.
โข Take a back sight QQโ on the staff held at the turning point Q. Measure the vertical
angle ฮฑ2.
R.L. of Qโ = R.L. of Q + QQโ
โข Take a foresight RRโ on the staff held at the point R without changing the vertical
angle ฮฑ2. Measure the sloping distance QR.
โด R.L. of R = R.L. of Qโ + QR sin ฮฑ2 โ RRโ
Thus,
R.L. of R = (R.L. of P + PPโ + PQ sin ฮฑ1 โ QQโ) + QQโ + (QR sin ฮฑ2 โ RRโ)