Civil Engineering 4th Semester Notes: Tacheometric Surveying and Curve Setting

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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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3. Tacheometric Surveying and Curve Setting

Tacheometric surveying is a rapid method of determining distances and elevations in the field without measuring the distance directly. It uses an instrument called a tacheometer, which is a special type of theodolite, to measure the distance based on the principle of angles and staff readings.

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3.1 Principles of Tacheometry

Tacheometry is based on the principle that the distance between the instrument and the staff can be determined by measuring the angle of elevation or depression and the staff reading.

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3.1.1 Tacheometer and its Component Parts

A Tacheometer is a type of theodolite equipped with special features for quick measurement of distances and elevations.

Components of a Tacheometer:

1. Telescope: Used for sighting the target.
2. Horizontal and Vertical Circles: For measuring horizontal and vertical angles.
3. Staff or Rod: A graduated rod held vertically at the point of observation.
4. Vernier Scales: For reading angles accurately.
5. Micrometer: For precise measurement of small distances.

Example: In road construction, a tacheometer is used to measure distances between survey points quickly without needing to physically measure each distance.

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3.1.2 Anallatic Lens

An anallatic lens is a special lens fitted to the telescope of the tacheometer that helps to eliminate the effect of staff height on the measurements. It ensures that the distance measurement remains accurate regardless of whether the staff is held at a particular height.

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3.2 Tacheometric Formula for Horizontal Distance with Telescope Horizontal and Staff Vertical

When the telescope is horizontal and the staff is vertical, the horizontal distance (D) can be calculated using the following formula:

$$D = k \times (S - C)$$

Where:

• $D$ = Horizontal distance
• $S$ = Staff reading (staff height)
• $C$ = Instrument constant
• $k$ = Tacheometric constant (depending on the instrument)

This formula helps calculate the horizontal distance when the staff is held vertically.

Example: If the staff reading is 3.5 meters, the instrument constant is 0.2, and the tacheometric constant is 100, the horizontal distance would be:

$$D = 100 \times (3.5 - 0.2) = 100 \times 3.3 = 330 \, \text{meters}$$

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3.3 Field Method for Determining Constants of Tacheometer

To determine the constants for a tacheometer, field measurements are taken with known distances and heights. The constants are calculated based on the observed staff readings and horizontal angles at different points.

Steps to determine the constants:

1. Measure a known distance: Use a tape measure to find the distance between two points.
2. Measure the staff reading: Using the tacheometer, measure the staff reading at the same points.
3. Calculate the constants: Use the formula to calculate the constants $C$ and $k$ based on the observed readings and known distances.

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3.4 Determining Horizontal and Vertical Distances with Tacheometer

3.4.1 Fixed Hair Method

In the Fixed Hair Method, the tacheometer is set up at a known point, and the readings are taken at different intervals as the staff is moved along the ground.

• Horizontal Distance (D) = $k \times (S - C)$
  
• Vertical Distance (V) = $\text{Staff reading} \times \tan(\text{Vertical angle})$
  

The constant values $k$ and $C$ are used to calculate the distances at each point.

Example: If the staff reading is 4 meters, the horizontal distance from the instrument is calculated using the formula mentioned earlier.

3.4.2 Staff Held Vertical

When the staff is held vertically, the readings are taken directly above the point of observation. This method simplifies the process of determining vertical distances.

• The horizontal distance and vertical distance can be measured using the same principles as the fixed hair method, but the staff is held vertically.

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3.5 Limitations of Tacheometry

Tacheometry has several limitations:

1. Accuracy: It may not be as accurate as direct measurement methods, especially for long distances.
2. Terrain Dependency: Tacheometric surveying can be difficult in rugged or heavily vegetated terrains.
3. Instrument Calibration: Requires proper calibration of the tacheometer for accurate readings.
4. Weather Conditions: Adverse weather conditions (fog, rain) can reduce accuracy.

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3.6 Types of Curves Used in Roads and Railway Alignments

In road and railway design, various types of curves are used to provide smooth transitions between straight sections of the track or road. These curves include:

1. Simple Curves: These are basic curves where the direction changes smoothly.
2. Compound Curves: These consist of two or more simple curves joined together.
3. Reverse Curves: Curves that change direction in the opposite way.
4. Transition Curves: Curves that gradually change from a straight line to a simple curve.

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3.7 Designation of Curves

Curves are designated by their radius (R), which defines the sharpness of the curve. A larger radius indicates a gentler curve, while a smaller radius indicates a sharper curve.

• Simple Circular Curve: A curve with a constant radius.
• Compound Curve: Curves with multiple radii.

Example: A curve with a radius of 500 meters would be a gentle curve, whereas one with a radius of 50 meters would be much sharper.

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3.8 Setting Simple Circular Curve

To set a simple circular curve, the following methods are commonly used:

3.8.1 Offsets from Long Chord

This method involves setting the curve by measuring offsets (perpendicular distances) from a long chord that connects the start and end of the curve.

Steps:

1. Measure the distance between the tangent points.
2. Calculate the offsets at regular intervals.
3. Set the curve using these offsets.

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3.8.2 Rankine’s Method of Deflection Angles

This method uses the deflection angle to set a simple circular curve. The deflection angle is the angle between the tangent at the starting point and the curve at any given point.

Formula:

$$\Delta = \frac{180}{\pi R}$$

Where $\Delta$ is the deflection angle and $R$ is the radius of the curve.

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Revision Points:

1. Tacheometric Surveying: A quick and effective method of measuring distances and elevations without direct distance measurements.
2. Anallatic Lens: A lens in the tacheometer to eliminate staff height errors.
3. Tacheometric Formula: The formula $D = k \times (S - C)$ is used to calculate horizontal distances.
4. Curve Types: Simple, compound, reverse, and transition curves are used in road and railway alignments.
5. Rankine’s Method: A method to set simple circular curves using deflection angles.

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Question & Answers

Q1: What is Tacheometric Surveying? A1: Tacheometric surveying is a method of measuring distances and elevations without directly measuring the distance. It uses a tacheometer to measure horizontal angles, vertical angles, and staff readings to calculate the distance.

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Q2: How does the Fixed Hair Method work? A2: In the Fixed Hair Method, the instrument is set up at a fixed point, and the readings are taken at different intervals as the staff is moved. The horizontal and vertical distances are calculated based on these readings.

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Q3: What is an anallatic lens? A3: An anallatic lens is a special lens fitted to the telescope of the tacheometer that helps eliminate errors caused by the height of the staff during measurement.

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Q4: What are the limitations of Tacheometry? A4: Tacheometry has limitations in terms of accuracy, terrain dependency, the need for proper calibration, and weather conditions that affect visibility.

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Q5: What is Rankine’s Method used for? A5: Rankine's Method is used to set a simple circular curve by calculating deflection angles at regular intervals along the curve.

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Diagrams:

1. Tacheometer Setup:
   

   • This diagram shows the tacheometer, staff, and instrument setup for measuring distances.

2. Simple Circular Curve Setup:
   

• This shows the layout of a simple circular curve using offsets from the long chord.

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