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.
Edm is a surveying instrument used to measure the distance electronically. This Surveying Instrument is used in triangulation to measure the length of Base line because more accuracy is required to measure the length of base line.
Edm is a surveying instrument used to measure the distance electronically. This Surveying Instrument is used in triangulation to measure the length of Base line because more accuracy is required to measure the length of base line.
Introduction, purpose, principle, instruments, methods of tacheometry, stadia constants, anallatic lens, Subtense bar, field work in tacheometry, reduction of readings, errors and precisions.
Course Contents:
Introduction; Linear measurements; Analysis and adjustment of measurements, Survey methods: coordinate systems, bearings, horizontal control, traversing, triangulation, detail surveying; Orientation and position; Areas and volumes; Setting out; Curve ranging; Global Positioning system (GPS); Photogrammetry.
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..
Introduction of surveying in Civil Engineering.MD Sakib Hasan
Did you know about surveying ? Surveying is an integral part of Civil Engineering discipline. you will able to know about ,what is surveying ? and learn about it can be use in many fields and for many purposes .
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 = 60°30′
, and the horizontal angle of PRQ = 68°18′
. The vertical
angle from P to Q =10°12′
, and the vertical angle from R to Q = 10°48′
.
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
Introduction, purpose, principle, instruments, methods of tacheometry, stadia constants, anallatic lens, Subtense bar, field work in tacheometry, reduction of readings, errors and precisions.
Course Contents:
Introduction; Linear measurements; Analysis and adjustment of measurements, Survey methods: coordinate systems, bearings, horizontal control, traversing, triangulation, detail surveying; Orientation and position; Areas and volumes; Setting out; Curve ranging; Global Positioning system (GPS); Photogrammetry.
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..
Introduction of surveying in Civil Engineering.MD Sakib Hasan
Did you know about surveying ? Surveying is an integral part of Civil Engineering discipline. you will able to know about ,what is surveying ? and learn about it can be use in many fields and for many purposes .
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 = 60°30′
, and the horizontal angle of PRQ = 68°18′
. The vertical
angle from P to Q =10°12′
, and the vertical angle from R to Q = 10°48′
.
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
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
Fractal dimensions of 2d quantum gravityTimothy Budd
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.
Plane and Applied surveying 2
Trigonometric Levelling Practical Part.
Report number(3)
Report name :
Apparatus
Theodolite instruments 1 No.
Range poles 1 No.
Tripod 2 Nos.
Surveyors’ pins 4 Nos.
Hammer 1 No.
Tape 1 No.
Object: The object is to measure the height of an inaccessible and accessible building using theodolite and measuring angles for the following cases:
1. Base of object is accessible.
2. Base of object is not accessible and the three points are on same vertical plane.
3. Base of object is not accessible and the three points are not on same vertical
plane.
-Procedure.
-Procedure for case 2.
-Procedure for case 3.
-Field Note Table.
Calculation For Case 1
I- If base of the object is accessible:
Calculation For Case 2
Case 2. The three points (A, B, and O) are on the same vertical plane.
-Calculations For case 3.
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
surveying_module-3-trigonometric-leveling by Denis Jangeed.pdfDenish Jangid
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
• There are main three cases to determine the
R.L of any point.
• Case : 1 :- Base of Object accessible.
• Case : 2 :- Base of object inaccessible,
instrument station 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.
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
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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
“Trigonometric levelling is the process of determining the differences of elevations of
stations from observed vertical angles and known distances.”
• The vertical angles are measured by means of theodolite.
• The horizontal distances by instrument
• Relative heights are calculated using trigonometric functions.
•If the distance between instrument station and object is small, correction for earth's
curvature and refraction is not required.
• 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.
•If the vertical angle is (+ve), the correction is taken as (+ve) & If the vertical angle is (-ve),
the correction is taken as (-ve)
TRIGONOMETRIC LEVELING
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3. Method of Observation
• There are two methods of observation:
1. Direct Method
2. Reciprocal method
1. Direct Method:
• 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.
• 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.
• Sometimes, the instrument is set on any suitable station and the height of instrument
axis is determined by taking back sight on B.M.
• Then the observation of the top of the tower is taken.
• 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.
• 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.
TRIGONOMETRIC LEVELING
SURVEYING
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4. Method of Observation
2. Reciprocal method:
• In this method, the instrument is set on each of the two stations, alternatively and
observations are taken.
• Let, Difference in elevation between two stations A & B is to be determined.
• First, set the instrument on A and take observation of B. Then set the instrument at
B and take observation of A.
• Set the theodolite on A and measure the angle of elevation of B as L BAC = α
• Set the theodolite on B and measure the angle of depression of A as L ABC’ = β
• Measure the horizontal distance between A & B as D using tape.
TRIGONOMETRIC LEVELING
SURVEYING
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6. Method of Observation
• If Distance between
A & B is Small,
AB' = AC = D
L ACB = 900
Similarly,
BA' = BC' = D
L AC'B = 900
BC = D tan α
AC' = D tan β
TRIGONOMETRIC LEVELING
SURVEYING
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7. Method of Observation
• If Distance between A & B is large,
• The correction for earth's curvature and refraction is required.
• Combined correction = 0.0673 D2, Where D = distance in KM.
• The difference in elevation between A & B,
H=BB'
=BC + CB'
=D tan α + 0.0673 D2. ....(1)
• If the angle of Depression B to A is measured,
AC'=D tan β [ BC'= D ]
• True difference in elevation between A & B,
H=AA'
= AC’ – A’C’
=D tan β - 0.0673 D2 ....(2)
TRIGONOMETRIC LEVELING
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8. Method of Observation
• Adding equation (1) & (2),
2 H = D tan α + D tan β
H = D/2 [tan α + D tan β] ..... (3)
• From equation (3), it can be seen that by reciprocal method of observation, the
correction for earth’s 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 α + D tan β]
TRIGONOMETRIC LEVELING
SURVEYING
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9. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
• 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.
TRIGONOMETRIC LEVELING
SURVEYING
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10. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
Case 1: Base of the object accessible:
TRIGONOMETRIC LEVELING
SURVEYING
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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.
α = Angle of elevation = L BAC
From fig.,
h = D tan α . ....(1)
R.L. of B = R.L. of B.M. + Bs + h
= R.L. of B.M. + Bs + D. tan α . ....(2)
• Now, when the distance between instrument station and object is large, then
correction for earth's curvature and refraction is required.
• combined correction = 0.0673 D2 Where D = distance in KM.
R.L. of B = R.L. of B.M. + Bs + D. tan α + 0.0673 D2
TRIGONOMETRIC LEVELING
SURVEYING
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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:
• 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.
• In this method, the instrument is set on the two different stations and the observations
of the object are taken.
• 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
TRIGONOMETRIC LEVELING
SURVEYING
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13. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
1. Instrument axes at the same level:
TRIGONOMETRIC LEVELING
SURVEYING
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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
α1 = Angle of elevation from A to P
α2 = Angle of elevation from B to P
From, Δ PA’P’ , h1 = D tan α1
. ....(1)
Δ PB’P’, h2 = (b + D) tan α2 ....(2)
• Equating (1) & (2),
D tan α1 = (b + D) tan α2
D tan α1 = b tan α2 + D tan α2
D (tan α1 - tan α2 ) = = b tan α2
D =
𝒃 𝒕𝒂𝒏 𝜶 𝟐
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
....(3)
TRIGONOMETRIC LEVELING
SURVEYING
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15. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
Substitute value of D in equation (1),
D =
𝐛 𝐭𝐚𝐧 𝛂 𝟏 𝐭𝐚𝐧 𝛂 𝟐
𝐭𝐚𝐧 𝛂 𝟏− 𝐭𝐚𝐧 𝛂 𝟐
....(4)
R.L. OF P = R.L. Of B.M. + Bs + h
TRIGONOMETRIC LEVELING
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16. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
2. Instrument axes at different levels:
• In the field, it is very difficult to keep the same height of instrument axis, at
different stations.
• 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.
• 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
TRIGONOMETRIC LEVELING
SURVEYING
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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:
TRIGONOMETRIC LEVELING
SURVEYING
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18. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
From, Δ PA’P’ , h1 = D tan α1
. ....(1)
Δ PB’P’’, h2 = (b + D) tan α2 ....(2)
Deducting equation (2) from equation (1)
h1 – h2 = D tan α1 - (b + D) tan α2
= D tan α1 - b tan α2 – D tan α2
hd = D (tan α1 - tan α2 ) –b tan α2 (hd = h1 - h2 )
hd + b tan α2 = D (tan α1 - tan α2 )
D =
𝐡 𝐝+ 𝐛 𝐭𝐚𝐧 𝛂 𝟐
𝐭𝐚𝐧 𝛂 𝟏− 𝐭𝐚𝐧 𝛂 𝟐
D =
(𝐛 + 𝐡 𝐝 𝐜𝐨𝐭 𝛂 𝟐) 𝐭𝐚𝐧 𝛂 𝟐
𝐭𝐚𝐧 𝛂 𝟏− 𝐭𝐚𝐧 𝛂 𝟐
...(3)
Substitute value of D in equation (1),
h1 = D tan α1
h1 =
(𝒃− 𝒉 𝒅 𝒄𝒐𝒕 𝜶 𝟐) 𝒕𝒂𝒏 𝜶 𝟏 𝒕𝒂𝒏 𝜶 𝟐
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
...(4)
TRIGONOMETRIC LEVELING
SURVEYING
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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:
TRIGONOMETRIC LEVELING
SURVEYING
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19
20. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
From, Δ PA’P’ , h1 = D tan α1
. ....(1)
Δ PB’P’’, h2 = (b + D) tan α2 ....(2)
Deducting equation (1) from equation (2)
h2 – h1 = (b + D) tan α2 - D tan α1
= b tan α2 + D tan α2 – D tan α1
hd = b tan α2 + D (tan α2 - tan α1) (hd = h1 - h2 )
hd - b tan α2 = D (tan α2 - tan α1)
- hd + b tan α2 = D (tan α1 - tan α2)
D =
𝒃 𝒕𝒂𝒏 𝜶 𝟐−𝒉 𝒅
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
D =
(𝒃− 𝒉 𝒅 𝒄𝒐𝒕 𝜶 𝟐) 𝒕𝒂𝒏 𝜶 𝟐
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
...(3)
Substitute value of D in equation (1),
h1 = D tan α1
h1 =
(𝒃− 𝒉 𝒅 𝒄𝒐𝒕 𝜶 𝟐) 𝒕𝒂𝒏 𝜶 𝟏 𝒕𝒂𝒏 𝜶 𝟐
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
...(4)
TRIGONOMETRIC LEVELING
SURVEYING
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21. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
TRIGONOMETRIC LEVELING
SURVEYING
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21
In above two cases, the equations of D and h1 are,
D =
(𝒃± 𝒉 𝒅 𝒄𝒐𝒕 𝜶 𝟐) 𝒕𝒂𝒏 𝜶 𝟐
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
h1 =
(𝒃± 𝒉 𝒅 𝒄𝒐𝒕 𝜶 𝟐) 𝒕𝒂𝒏 𝜶 𝟏 𝒕𝒂𝒏 𝜶 𝟐
𝒕𝒂𝒏 𝜶 𝟏− 𝒕𝒂𝒏 𝜶 𝟐
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:
TRIGONOMETRIC LEVELING
SURVEYING
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23. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
TRIGONOMETRIC LEVELING
SURVEYING
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Let A and B be the two instrument stations not in the same vertical plane as that of P.
Procedure:
• Select two survey stations A and B on the level ground and measure b as the horizontal
distance between them.
• 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.
• Measure the angle of elevation α1 to P.
• Measure the horizontal angle at A, L BAC = θ
• Shift the instrument to B and Measure the angle of elevation α2 to P.
• Measure the horizontal angle at B as α.
24. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
TRIGONOMETRIC LEVELING
SURVEYING
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α1 = angle of elevation from A to P
α2 = angle of elevation from B to P
Θ = Horizontal angle L BAC at station A (clockwise)
α = 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 Δ ABC, L BAC = Θ
L ABC = α
So, L ACB = 180 – (Θ + α)
AB = b
25. METHODS OF DETERMINING THE ELEVATION OF A POINT
BY THEODOLITE
TRIGONOMETRIC LEVELING
SURVEYING
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25
We know, three angles and one side of Δ ABC. Therefore using Sine Rule, we can calculate distance AC & BC
as below.
BC =
𝒃 𝒔𝒊𝒏 𝜽
𝐬𝐢𝐧 [𝟏𝟖𝟎− 𝜽+𝛂 ]
……(1)
Ac =
𝒃 𝒔𝒊𝒏 𝜶
𝐬𝐢𝐧 [𝟏𝟖𝟎− 𝜽+𝛂 ]
……(2)
Now, h1= AC tan α1 & h2= BC tan α2
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
TRIGONOMETRIC LEVELING
SURVEYING
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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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• Set up the theodolite at some convenient point O1 midway between P and Q.
• Measure the vertical angle α1 to the station P. Also measure the horizontal distance
D1 between O1 and P.
• Similarly, measure the vertical angle β1 to the station Q. also measure the
horizontal distance D2 between O1 and Q.
• Determine the difference in elevation H1 between P and Q as explained below.
• Let us assume that,
α1 = angle of depression
β1 = angle of elevation
H1 = PP” +QQ”
= (PP’ – P’P”) + (QQ’ + Q’Q”)
= (D1 tan α1 - C1) + (C2 + D2 tan β1) … … … (1)
• Where C1 and C2 are the corrections due to curvature of earth and refraction.
28. INDIRECT LEVELLING ON A ROUGH TERRAIN
TRIGONOMETRIC LEVELING
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• As the distances D1 and D2 are nearly equal, the corrections C1 and C2 are also approximately
equal.
∴ H1 = D1 tan α1 + D2 tan β1 … … … (2)
• Now shift the instrument to the station O2 midway between Q and R.
• Measure the vertical angles α2 and β2 to the stations Q and R and respective
horizontal distance D3 and D4.
∴ Difference of elevations between Q and R is,
H2 = D3 tan α2 + D4 tan β2 … … … (3)
• Repeat the above process at the station O3
∴ H3 = D5 tan α3 + D6 tan β3 … … … (4)
• Determine the difference in elevations of P and S as,
H = H1 + H2 + H3
• ∴R.L. of S = R.L. of P + H
29. INDIRECT LEVELLING ON A ROUGH TERRAIN
TRIGONOMETRIC LEVELING
SURVEYING
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• Indirect levelling is not as accurate as direct levelling with a levelling instrument. The
method is used in rough country.
• If back sight and foresight distances are approximately equal, the effect of curvature and
refraction is eliminated.
30. INDIRECT LEVELLING ON A STEEP TERRAIN
TRIGONOMETRIC LEVELING
SURVEYING
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• If the ground is quite steep, the method of indirect levelling can be used with
advantage.
31. INDIRECT LEVELLING ON A STEEP TERRAIN
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• The following procedure can be used to determine the difference of elevations between P
and R.
• Set up the instrument at a convenient station O1 on the line PR.
• Make the line of collimation roughly parallel to the slope of the ground. Clamp the
telescope.
• Take a back sight PP’ on the staff held at P. Also measure the vertical angle α1 to P’.
Determine R.L. of P’ as.
R.L. of P’ = R.L. of P + PP’
• Take a foresight QQ’ on the staff held at the turning point Q. without changing the vertical
angle α1. Measure the slope distance PQ between P and Q.
R.L. of Q = R.L. of P’ + PQ sin α1 – QQ’
OR
R.L. of Q = R.L. of P + PP’ + PQ sin α1 – QQ’
32. INDIRECT LEVELLING ON A STEEP TERRAIN
TRIGONOMETRIC LEVELING
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• 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.
• Take a back sight QQ” on the staff held at the turning point Q. Measure the vertical
angle α2.
R.L. of Q” = R.L. of Q + QQ”
• Take a foresight RR’ on the staff held at the point R without changing the vertical
angle α2. Measure the sloping distance QR.
∴ R.L. of R = R.L. of Q” + QR sin α2 – RR’
Thus,
R.L. of R = (R.L. of P + PP’ + PQ sin α1 – QQ’) + QQ” + (QR sin α2 – RR’)