Bearing and Included Angle of a Closed Traverse
In surveying, a traverse is a series of connected lines whose lengths and directions are measured in the field. When the traverse forms a closed figure, it is called a closed traverse. Understanding bearings and included angles is essential for accurate plotting and calculation. In ITI Draughtsman Civil, this topic is important for map preparation and layout design.
1. Bearing
Definition
Bearing is the horizontal angle measured between a survey line and a reference direction, usually the magnetic north or true north.
Types of Bearing
(a) Whole Circle Bearing (WCB)
- Measured clockwise from north.
- Ranges from 0° to 360°.
(b) Reduced Bearing (RB) or Quadrantal Bearing
- Measured from north or south towards east or west.
- Ranges from 0° to 90°.
- Expressed as N–E, S–E, S–W, N–W.
Fore Bearing (FB) and Back Bearing (BB)
- Fore Bearing: Bearing of a line in the forward direction.
- Back Bearing: Bearing of the same line in the reverse direction.
- BB = FB ± 180°
2. Closed Traverse
A closed traverse is a series of connected lines that form a closed polygon. It starts and ends at the same point or at two known points.
Types of Closed Traverse
- Loop Traverse: Starts and ends at the same point.
- Link Traverse: Starts and ends at different known points.
3. Included Angle
Definition
The included angle is the angle between two consecutive survey lines in a traverse. It is measured at the point where the two lines meet.
Calculation of Included Angle
The included angle can be calculated using the bearings of adjacent lines:
- Included Angle = Back Bearing of previous line – Fore Bearing of next line
- If the result is negative, add 360°.
4. Relationship Between Bearings and Included Angles
In a closed traverse, bearings and included angles are related to each other. The sum of included angles depends on the number of sides of the traverse.
- For a closed traverse with n sides:
- Sum of included angles = (2n – 4) × 90°
This rule helps in checking the accuracy of field measurements.
5. Procedure for Determining Bearings and Included Angles
- Measure the fore bearings of all lines using a compass.
- Calculate back bearings.
- Determine included angles using the formula.
- Check the sum of included angles for accuracy.
6. Importance of Bearings and Included Angles
- Helps in accurate plotting of traverse.
- Used in calculation of coordinates and areas.
- Essential for checking survey accuracy.
- Used in layout of roads, boundaries, and structures.
7. Errors in Traverse
Errors may occur due to incorrect measurement of bearings or angles.
- Magnetic errors in compass readings.
- Improper alignment of survey lines.
- Human errors in observation and recording.
Role of Draughtsman Civil
A Draughtsman Civil uses bearings and included angles to plot traverses accurately on drawings. Proper understanding helps in preparing site layouts and engineering plans.
Conclusion
Bearings and included angles are key elements in traverse surveying. They help in determining the direction and shape of the survey area. Accurate calculation ensures correct mapping and construction planning.
For ITI Draughtsman Civil students, mastering this topic is essential for successful surveying and drafting work.