Traversing using Theodolite, Traverse Computation, Coordinates, Balancing, Gale’s Traverse Table, Area & Omitted Measurements

Traversing using Theodolite, Traverse Computation, Coordinates, Balancing, Gale’s Traverse Table, Area & Omitted Measurements

Traversing is an important method in surveying where a series of connected lines are measured using a theodolite. It is widely used for mapping, boundary surveys, and construction work. Understanding traverse computation, coordinate determination, balancing, and area calculation is essential for Surveyor trade trainees.

Traversing using Theodolite

In theodolite traversing, both angles and distances are measured. The directions are obtained using theodolite, while distances are measured using chain or tape.

Types of Traverse

1. Closed Traverse

• Forms a closed polygon
• Starts and ends at the same point
• Used for boundary and land surveys

2. Open Traverse

• Does not return to starting point
• Used for roads, canals, pipelines
• Cannot be checked directly for errors

Traverse Computation

Traverse computation involves calculating bearings, latitudes, departures, and coordinates of survey points.

Latitude and Departure

• Latitude (L): North-South component of a line
• Departure (D): East-West component of a line

Formulas:

• Latitude = Length × cos(θ)
• Departure = Length × sin(θ)

Determination of Consecutive Coordinates

Coordinates of points are calculated successively from one station to another using latitude and departure values.

• Northing = Previous Northing + Latitude
• Easting = Previous Easting + Departure

Independent Coordinates

Independent coordinates are calculated with respect to a fixed reference point (origin). All points are located based on their distance from this origin.

Checking of Traverse

In a closed traverse:

• Sum of latitudes = 0
• Sum of departures = 0

If not zero, there is a closing error.

Balancing of Traverse

Balancing is the process of distributing closing error among all survey lines.

Bowditch’s Method

• Correction ∝ Length of line
• Used when linear and angular measurements are equally accurate

Transit Method

• Correction ∝ Latitude or Departure
• Used when angular measurements are more accurate

Gale’s Traverse Table

Gale’s table is used to record and compute traverse data systematically.

Computation of Area using Coordinates

Area can be calculated using coordinate method:

Area = 1/2 [Σ (X₁Y₂ − X₂Y₁)]

Where X and Y are coordinates of points.

Calculation of Omitted Measurements

Sometimes measurements like length or bearing of a line may be missing. These can be calculated using known data:

• Using latitude and departure equations
• Using coordinate differences
• Applying traverse conditions

Importance in Surveyor Trade

• Used in land and boundary surveys
• Essential for mapping and plotting
• Helps in accurate calculation of area
• Important for construction projects

Precautions

• Ensure accurate measurement of angles and distances
• Check calculations carefully
• Apply proper balancing methods
• Maintain neat and clear tables

Conclusion

Traversing using theodolite is a fundamental method in surveying. Understanding computation, coordinate calculation, balancing, and area determination ensures accurate survey results.

For ITI Surveyor trainees, mastering these concepts is essential for professional surveying work and real-world applications.