Conversion of Bearing (WCB to R.B.)
In compass surveying, bearings are used to represent the direction of survey lines. Bearings can be expressed in two main systems: Whole Circle Bearing (WCB) and Reduced Bearing (R.B.), also known as Quadrantal Bearing (QB). Understanding the conversion between these systems is essential for accurate surveying and plotting.
Whole Circle Bearing (WCB)
Whole Circle Bearing is measured clockwise from the north direction. It ranges from 0° to 360°.
- Measured in clockwise direction
- Starts from North (0°)
- Ends at 360°
Reduced Bearing (R.B.) / Quadrantal Bearing
Reduced Bearing is measured from either North or South towards East or West. The value of R.B. always lies between 0° and 90°.
- Measured from North or South
- Direction indicated by E or W
- Value ranges from 0° to 90°
Need for Conversion
In surveying work, sometimes bearings are recorded in WCB format but need to be converted into R.B. for easier interpretation and plotting. Conversion helps in understanding the direction of survey lines more clearly.
Conversion Rules (WCB to R.B.)
The conversion depends on the quadrant in which the bearing lies:
| WCB Range | Quadrant | Reduced Bearing (R.B.) |
|---|---|---|
| 0° to 90° | NE | N θ E (same value) |
| 90° to 180° | SE | S (180° − θ) E |
| 180° to 270° | SW | S (θ − 180°) W |
| 270° to 360° | NW | N (360° − θ) W |
Examples of Conversion
Example 1:
WCB = 40°
R.B. = N 40° E (NE quadrant)
Example 2:
WCB = 120°
R.B. = S (180° − 120°) E = S 60° E
Example 3:
WCB = 220°
R.B. = S (220° − 180°) W = S 40° W
Example 4:
WCB = 300°
R.B. = N (360° − 300°) W = N 60° W
Steps for Conversion
- Identify the quadrant of the given WCB
- Apply the appropriate formula
- Write the result in N/S and E/W format
Advantages of Reduced Bearing
- Easy to understand direction
- Simple for plotting on drawing sheet
- Useful in fieldwork calculations
Precautions
- Always identify the correct quadrant
- Use correct formula for conversion
- Maintain proper notation (N/S, E/W)
- Avoid calculation errors
Application in Surveyor Trade
Conversion of WCB to R.B. is widely used in compass surveying, plotting of traverses, and preparation of maps. It helps surveyors interpret directions accurately and perform calculations efficiently.
Conclusion
Understanding the conversion of bearings from Whole Circle Bearing to Reduced Bearing is essential for surveyors. It simplifies direction representation and improves accuracy in surveying work. For ITI Surveyor trainees, mastering this concept is important for both field and office applications.