Theodolite Surveying 🌍🧭

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For 4th Semester Polytechnic CE Students
Written by Garima Kanwar | Blog: Rajasthan Polytechnic
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Subject: Advanced Surveying CE 4002(Same as CC 4002)

Branch: Civil Engineering 🏗️
Semester: 4th Semester 📚
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2.1 Types and Uses of Theodolite

A theodolite is an instrument used to measure horizontal and vertical angles with great precision. It's essential in surveying because it helps surveyors accurately measure the angles between lines. There are two main types of theodolites:

1. Transit Theodolite 🧭

Description: It is the most widely used type in surveying today.
Functionality: The telescope in a transit theodolite can be rotated 360° horizontally and 180° vertically. This allows the instrument to be used to measure angles both from the left and right sides.
Uses:
- Land surveys for construction projects like roads, buildings, and bridges.
- Railway alignments and road alignment.
- Mapping and boundary setting.

2. Non-Transit Theodolite

Description: This type has a fixed telescope that does not rotate 360° horizontally. It is less accurate compared to the transit theodolite.
Uses:
- Simple survey tasks where full rotation is not needed.

Diagram for Theodolite:

               |
       _____________
      |     T       |
      |   Telescope  |
      |______________|
         ||   ||
   Horizontal Circle
         ||
     Leveling Screws

2.2 Components of Transit Theodolite and Their Functions

A transit theodolite consists of several important parts that help measure angles accurately. Let’s look at each of them:

1. Telescope 🔭

The telescope is used to sight the object or point whose angle you want to measure.
It can rotate horizontally and vertically to help you sight the object from any direction.

2. Horizontal Circle 🌀

This is a circular graduated scale that measures horizontal angles.
It’s marked in degrees (°) and minutes (’).

3. Vertical Circle 🔵

This scale measures vertical angles (elevation or depression) and is similar to the horizontal circle but oriented vertically.

4. Vernier Scale 📏

The Vernier scale is a small scale that’s placed along the horizontal or vertical circle to help you read angles more precisely.
It measures fractions of the smallest divisions on the main scale, increasing the instrument's precision.

5. Leveling Screws 🔧

These are used to level the instrument. If the instrument is not level, the angle measurements will be inaccurate.

6. Plumb Bob ⛓️

A plumb bob is used to ensure that the instrument is directly above the survey point.
It hangs from the instrument and helps in proper alignment.

Diagram for Components of Transit Theodolite:

                  _______
                |       | Telescope
                |_______|
                    ||
  Horizontal Circle/Leveling Screws
                    ||
                 Plumb Bob
                    ||
            Leveling Screws

2.3 Reading the Vernier of Transit Theodolite

The Vernier Scale allows us to read angles more accurately than just using the main scale.

Steps to read Vernier:

Main Scale Reading: First, look at the main scale and note down the number that is directly in line with the zero mark of the Vernier scale.
Vernier Scale Reading: Look for the division on the Vernier scale that aligns exactly with any division on the main scale.
Final Angle Calculation: Add the main scale reading and the Vernier scale reading to get the final angle.

Example:
If the main scale reads 30°, and the Vernier scale shows 15 minutes (after you match the lines), the final angle will be 30° 15'.

2.4 Technical Terms in Theodolite Surveying

These are essential terms used in the operation of a theodolite:

2.4.1 Swinging

Swinging means rotating the telescope in the horizontal plane to sight different objects or points.

2.4.2 Transiting

Transiting refers to turning the telescope 180° so that it faces in the opposite direction. This is done to switch between the "face left" and "face right" positions.

2.4.3 Face Left

This refers to when the telescope is turned to the left side of the instrument. In this position, the readings are taken in one direction.

2.4.4 Face Right

This refers to when the telescope is turned to the right side of the instrument. Readings are taken in the opposite direction.

2.5 Fundamental Axes of Transit Theodolite and Their Relationship

The axes are important because they determine the rotation and measurement of angles:

Horizontal Axis:
- The axis around which the horizontal circle rotates to measure horizontal angles.
Vertical Axis:
- The axis that the telescope rotates around to measure vertical angles.
Line of Sight:
- The straight line passing through the center of the telescope. It points toward the object being measured.

Diagram for Fundamental Axes:

       Horizontal Axis
            ↑
    ________________
   |                | Telescope
   |________________|
            ↓
        Vertical Axis

2.6 Temporary Adjustment of Transit Theodolite

Before using the theodolite in the field, you must perform temporary adjustments to ensure accurate readings:

Level the Instrument:
Use the leveling screws to make sure the instrument is perfectly horizontal.
Align the Telescope:
The telescope should be aligned with a known reference point, such as a survey marker.
Plumb the Instrument:
Ensure the instrument is directly above the survey point by using the plumb bob.

2.7 Measurement of Horizontal Angle

2.7.1 Direct Method

In the direct method, you set the instrument at a reference point and directly read the angle from the horizontal circle.

2.7.2 Repetition Method

This method involves taking multiple measurements of the same angle and averaging them to reduce errors.

2.7.3 Errors Eliminated by Repetition Method

The repetition method reduces errors like instrumental errors or reading errors by averaging out multiple readings.

2.8 Measurement of Magnetic Bearing of a Line

2.8.1 Prolonging a Line

This refers to extending an existing line beyond its end point to a new location.

2.8.2 Deflection Angle

A deflection angle is the angle formed between the continuation of a line and the new direction of the line.

2.9 Theodolite Traversing

Traversing is the process of using a theodolite to measure angles and distances to establish a survey path.

2.9.1 Included Angle Method

In this method, the included angles between consecutive lines are measured to determine the positions of different points.

2.9.2 Deflection Angle Method

Here, deflection angles from the previous line are measured at each station to help determine the survey path.

2.10 Checks for Open and Closed Traverse

Open Traverse

In an open traverse, the survey does not form a closed loop. Errors can be reduced by correcting the bearing or adjusting the positions.

Closed Traverse

In a closed traverse, the starting and ending points meet. Any errors in angle or distance can be corrected by adjusting the coordinates of the points.

2.11 Calculation of Bearing from Angles

To calculate the bearing of a line:

Measure the azimuth (angle of the line from a reference point).
Convert it into bearing (compass direction like N, S, E, W).

2.12 Traverse Computation

Latitude and Departure:
- Latitude: North-south component of the distance.
- Departure: East-west component of the distance.
Consecutive Coordinates and Independent Coordinates:
- Consecutive coordinates are computed relative to each station.
- Independent coordinates are computed from known reference points.

2.13 Balancing the Traverse

2.13.1 Bowditch’s Rule

Used to distribute errors proportionally in an open traverse.

2.13.2 Transit Rule

Used to correct errors in a closed traverse, distributing them based on the distance between stations.

Review Points 🔍

The transit theodolite is widely used for measuring horizontal and vertical angles.
The Vernier scale enhances the accuracy of readings.
Traversing helps surveyors establish the exact position of various points by measuring angles and distances.
Temporary adjustments are important to ensure accuracy before starting the survey.

Questions and Answers ❓

Q1: How do you measure a vertical angle using theodolite?
A1: The vertical angle is measured using the vertical circle of the theodolite. The telescope is aimed at the object, and the angle between the line of sight and the horizontal plane is read.

Q2: What is the purpose of using the Repetition Method in angle measurement?
A2: The Repetition Method is used to reduce errors by taking multiple measurements of the same angle and averaging them, improving accuracy.

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