10. Theodolite in Surveying

 

THEODOLITE IN SURVEYING

1. Definition

A theodolite is a precision surveying instrument used to measure horizontal angles, vertical angles, and in modern instruments, even distances.

It is mainly used in:

• Traversing

• Triangulation

• Alignment of roads, bridges, tunnels

• Setting out works

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2. Purpose of Using a Theodolite

A theodolite is used to:

• Measure horizontal and vertical angles accurately

• Establish straight lines and right angles

• Determine elevations

• Do tacheometric surveying

• Set out curves, foundations, columns, and center lines

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3. Types of Theodolites

(a) Transit Theodolite

The telescope can be rotated fully in vertical plane (180°).
➡️ Most commonly used today.

(b) Non-Transit Theodolite

Telescope cannot be fully rotated.
➡️ Now almost obsolete.

(c) Digital Theodolite

Angles are shown digitally on screen.
➡️ Faster, more accurate, easy to use.

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4. Main Parts of a Theodolite

A) Telescope

Used for sighting the object.

B) Vertical Circle

Measures vertical angles.

C) Horizontal Circle

Measures horizontal angles.

D) Levelling Head

Used to level the instrument using foot screws.

E) Tribrach

Base plate for fixing the instrument on tripod.

F) Plumb Bob / Optical Plummet

Used for centering the instrument over station point.

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5. Temporary Adjustments of a Theodolite

Before taking observations, three adjustments are necessary:

1. Setting up – Fixing instrument on tripod

2. Centering – Bringing instrument exactly over station point

3. Levelling – Making vertical axis truly vertical

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6. Permanent Adjustments (Theory)

These ensure:

• Line of collimation is perpendicular to trunnion axis

• Trunnion axis is perpendicular to vertical axis

• Vertical circle reads zero when telescope is horizontal

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7. Measurement of Angles

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A) Measurement of Horizontal Angle

Steps:

1. Set up, center, and level the theodolite.

2. Set zero on horizontal circle.

3. Sight first point A and clamp.

4. Turn telescope to sight second point B.

5. Read the angle on horizontal circle.

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B) Measurement of Vertical Angle

Steps:

1. Level instrument carefully.

2. Sight the object.

3. Read vertical circle.

4. Angle of elevation or depression is obtained.

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8. Applications of Theodolite

• Traversing

• Triangulation

• Setting out right angles

• Alignment of roads and railways

• Tunneling and bridge works

• Height determination

• Curve setting

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9. Numerical Example

Example: Measurement of Height of a Tower Using Theodolite

Given:

• Distance from tower base = 30 m

• Angle of elevation to top = 35°

• Height of instrument = 1.5 m

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Step 1: Use trigonometric relation

$$\tan \theta = \frac{h}{d}$$ $$h = d \tan \theta$$ $$h = 30 \times \tan 35^\circ$$ $$h = 30 \times 0.7002 = 21.01 \text{ m}$$

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Step 2: Add height of instrument

$$\text{Total height of tower} = 21.01 + 1.5$$ $$= 22.51 \text{ m}$$

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Final Answer

Height of the tower = 22.5 m (approx.)

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10. Advantages of Theodolite

• High accuracy

• Suitable for large projects

• Measures both horizontal & vertical angles

• Can be used for distance measurement (tacheometry)

• Long life and reliability

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11. Limitations

• Requires skilled operator

• Time-consuming compared to total station

• Needs frequent adjustments

• Digital models depend on battery

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12. Difference: Theodolite vs Total Station

Feature	Theodolite	Total Station
Angle measurement	Yes	Yes
Distance measurement	Limited	Yes (EDM)
Data storage	No	Yes
Speed	Moderate	Very fast
Cost	Lower	Higher

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