Problems in Transit Theodolite – Departure, Latitude, Northing and Easting
In theodolite surveying, especially in traverse calculations, it is important to determine the position of points using angular and linear measurements. Terms like departure, latitude, northing, and easting are used to represent the direction and distance of survey lines. In ITI Draughtsman Civil, understanding these concepts is essential for solving traverse problems and plotting accurately.
1. Latitude
Definition
Latitude is the projection of a survey line on the north-south direction.
- If the line moves towards north → North Latitude (+)
- If the line moves towards south → South Latitude (−)
Formula
- Latitude = Length × cos(θ)
2. Departure
Definition
Departure is the projection of a survey line on the east-west direction.
- If the line moves towards east → East Departure (+)
- If the line moves towards west → West Departure (−)
Formula
- Departure = Length × sin(θ)
3. Northing and Easting
Definition
- Northing: Total distance of a point measured in the north direction from a reference point.
- Easting: Total distance of a point measured in the east direction from a reference point.
These are cumulative values obtained by adding latitudes and departures.
4. Calculation of Northing and Easting
- Northing = Sum of all north latitudes − Sum of all south latitudes
- Easting = Sum of all east departures − Sum of all west departures
5. Sign Convention
| Direction | Latitude | Departure |
|---|---|---|
| North-East (NE) | + | + |
| South-East (SE) | − | + |
| South-West (SW) | − | − |
| North-West (NW) | + | − |
6. Application in Traverse Problems
- Used to calculate coordinates of survey points.
- Helps in plotting traverse accurately.
- Used in adjustment of closed traverse.
- Essential for map preparation and layout design.
7. Example (Simple Concept)
If a line of length 100 m makes an angle of 30° with the north direction:
- Latitude = 100 × cos(30°)
- Departure = 100 × sin(30°)
These values help in determining the position of the next survey point.
8. Importance
- Provides accurate positioning of points.
- Helps in solving traverse problems.
- Essential for engineering design and construction.
Precautions
- Use correct angle measurements.
- Apply proper sign conventions.
- Check calculations carefully.
Role of Draughtsman Civil
A Draughtsman Civil uses latitude and departure values to plot survey points and prepare accurate layouts. Understanding these concepts ensures precise drawings and construction planning.
Conclusion
Latitude, departure, northing, and easting are essential concepts in theodolite surveying. They help in determining the position of points and solving traverse problems accurately.
For ITI Draughtsman Civil students, mastering these calculations is important for accurate surveying and successful engineering work.