Bearing Systems in Survey Lines
Surveyors use two primary systems to designate the bearings of survey lines:
- Whole Circle Bearing System (W.C.B.)
- Quadrantal Bearing System (Q.B.)
Whole Circle Bearing System (W.C.B.)
The Whole Circle Bearing System, also known as the Azimuthal system, is a method used in surveying to express the direction of survey lines relative to a fixed reference direction, typically true north or magnetic north. This system offers a comprehensive and unambiguous way of describing directions, making it invaluable in various surveying and navigation applications.
Reference Direction
In the W.C.B. system, bearings are measured from a single reference direction, usually true north or magnetic north. This provides a consistent starting point for all measurements.
Measurement Direction
Bearings are always measured in a clockwise direction from the reference direction. This standardized approach eliminates any ambiguity in the direction of measurement. The W.C.B. system uses the entire 360° of a circle, allowing for precise and unique descriptions of any direction.
Prismatic Compass Compatibility
Prismatic compasses are typically graduated using the W.C.B. system, making field measurements straightforward and directly applicable.
Notation
Whole Circle Bearings are typically denoted as a single angle value, ranging from 0° to 360°. For example:
– 45° (Northeast direction)
– 180° (South direction)
– 270° (West direction)
Consider a point O with four lines extending from it:
1. Line OA: 45°
– This line is 45° clockwise from North
2. Line OB: 135°
– This line is 135° clockwise from North (Southeast direction)
3. Line OC: 225°
– This line is 225° clockwise from North (Southwest direction)
4. Line OD: 315°
– This line is 315° clockwise from North (Northwest direction)
∠NOA = θ₁ = 45°
∠NOB = θ₂ = 135°
∠NOC = θ₃ = 225°
∠NOD = θ₄ = 315°
Advantages of W.C.B.:
- Precision: Offers more precise readings due to its 360° range.
- Unambiguous: Each bearing has a unique value, reducing the chance of misinterpretation.
- Ease of calculation: Simplifies certain survey calculations and computations.
The Whole Circle Bearing system is particularly useful in modern surveying techniques, including those that use GPS and other digital technologies, due to its straightforward numerical representation and ease of integration with computerized systems.
Limitations
- Conversion Needed: When working with other bearing systems, conversions may be necessary.
- Initial Setup: Proper identification of the reference direction (true or magnetic north) is crucial for accurate measurements
Applications
- The W.C.B. system finds wide application in:
– Land surveying and mapping
– Navigation (both marine and terrestrial)
– Construction and engineering projects
– Geographic Information Systems (GIS)
– GPS and other satellite-based positioning systems
The Quadrantal Bearing System
The quadrantal bearing system is a method used in surveying to express the direction of survey lines relative to the cardinal directions of North and South. This system offers a more intuitive approach compared to other bearing systems, making it particularly useful for surveyors and navigators.
Reference Meridians
In the quadrantal bearing system, both North and South directions serve as reference meridians. This is a key differentiator from systems that use only North or only South as a reference.
Measurement Direction
Bearings are measured either eastward or westward from the nearest reference meridian (North or South). This approach minimizes the angular measure, never exceeding 90°
Clockwise vs. Anticlockwise
The direction of measurement (clockwise or anticlockwise) depends on the position of the line relative to the reference meridian. This flexibility allows for more intuitive bearing descriptions.
Quadrant Specification
To uniquely identify a line’s direction, the system specifies the quadrant in which the line lies. This eliminates any ambiguity that might arise from the angle measurement alone.
Notation
Quadrantal bearings are typically denoted in the following format:
[Reference Meridian] [Angle] [Direction]
For example:
- N 45° E (North 45 degrees East)
- S 30° W (South 30 degrees West)
Examples
Consider a point O with four lines extending from it:
- Line OA: N 30° E
- This line is 30° east of North
- Line OB: S 45° E
- This line is 45° east of South
- Line OC: S 60° W
- This line is 60° west of South
- Line OD: N 75° W
- This line is 75° west of North
Line OA: N 30° E (30° east of North)
Line OB: S 45° E (45° east of South)
Line OC: S 60° W (60° west of South)
Line OD: N 75° W (75° west of North)
Advantages
- Intuitive Reading: The system provides a more natural way of describing directions, especially for those familiar with compass directions.
- Reduced Angles: By using the nearest cardinal direction as a reference, the system ensures that angles never exceed 90°, simplifying calculations and reducing the chance of errors.
- Unambiguous: The quadrant specification eliminates any potential confusion about the line’s exact direction.
- Compatibility: The system is directly compatible with the graduations on a surveyor’s compass, facilitating field work.
Limitations
- Conversion Needed: When working with other bearing systems or performing certain calculations, quadrantal bearings may need to be converted to whole-circle bearings or azimuths.
- Potential for Error: The use of four different reference directions (N, S, E, W) can lead to errors if not carefully noted and interpreted.
Applications
The quadrantal bearing system finds wide application in:
- Land surveying
- Navigation (both marine and terrestrial)
- Cartography
- Orienteering and outdoor activities
Conversion of Bearings From one system to another
| Case | W.C.B. between | Rule of Q.B. | Quadrant |
|---|---|---|---|
| I | 0° and 90° | W.C.B. | N.E. |
| II | 90° and 180° | 180° − W.C.B. | S.E. |
| III | 180° and 270° | W.C.B. − 180° | S.W. |
| IV | 270° and 360° | 360° − W.C.B. | N.W. |
Note: When a line lies exactly either along North, South, East or West, the W.C.B. of the line is converted in the quadrantal system as follows:
- If W.C.B. of a line = 0° then, Q.B. of the line is N.
- W.C.B. of a line = 90° then, Q.B. of the line is E 90°.
- W.C.B. of a line = 180° then, Q.B. of the line is S.
- W.C.B. of a line = 270° then, Q.B. of the line is W 90°.
| Case | R.B. | Rule for W.C.B. | W.C.B. between |
|---|---|---|---|
| I | N α E | R.B. | 0° and 90° |
| II | S β E | 180° − R.B. | 90° and 180° |
| III | S γ W | 180° + R.B. | 180° and 270° |
| IV | N δ W | 360° − R.B. | 270° and 360° |
