Compass surveying is a fundamental technique in the field of land surveying, relying heavily on the accurate measurement of bearings to determine the direction of survey lines. Bearings provide a standardized method for describing the orientation of a line relative to a reference direction, ensuring consistency and precision in survey work. Among the various bearing notations, the Whole Circle Bearing (WCB) system and the Quadrantal Bearing System (QBS) are the most widely used. This article delves into these two systems, elucidating their definitions, applications, and the seamless conversion between them.
Bearing and Angles
In the realm of surveying, bearings play a crucial role in delineating the direction of survey lines. Bearings can be measured in two primary ways:
- Relation to Another Survey Line: This method involves measuring the angle between two survey lines. The resulting angle provides information about the relative orientation of the lines but does not specify their absolute direction relative to a fixed reference.
- Relation to the Meridian: Alternatively, bearings can be measured with respect to a meridian, providing an absolute directional reference. This method defines the bearing as the direction of a line relative to a specified meridian, such as the true north or magnetic north.
Understanding the distinction between these two methods is essential for accurate and meaningful surveying.
Types of Meridians
A meridian is a reference line used in surveying to determine bearings. There are three primary types of meridians:
True Meridian
The true meridian is a geographic line that passes through the true north and south poles of the Earth. It is defined by the intersection of the Earth’s surface with the plane that contains the rotational axis. In practical terms, the true meridian at any given point is the line that aligns with the direction of true north.
- True Bearing: The true bearing of a survey line is the horizontal angle between the line and the true meridian passing through one of its endpoints. This measurement provides an absolute direction based on the Earth’s geographic poles.
Magnetic Meridian
The magnetic meridian is determined by the Earth’s magnetic field. It is the direction indicated by a freely suspended and balanced magnetic needle, which aligns itself with the Earth’s magnetic field lines.
- Magnetic Bearing: The magnetic bearing of a survey line is the horizontal angle between the line and the magnetic meridian passing through one of its endpoints. To obtain an accurate magnetic bearing, it is essential to use a magnetic compass free from any external magnetic influences.
Arbitrary Meridian
In certain surveying scenarios, establishing a convenient and practical reference direction is necessary. This leads to the creation of an arbitrary meridian, which is a direction based on a permanent or commonly visible mark or signal within the survey area.
- Arbitrary Bearing: The arbitrary bearing is the horizontal angle between the survey line and the arbitrary meridian passing through one of its endpoints. This system is particularly useful for determining the relative positions of survey lines when a true or magnetic meridian is impractical.
Bearing Systems in Surveying
Surveying employs different bearing systems to describe the direction of survey lines accurately. The two most common systems are:
- Whole Circle Bearing (WCB) System
- Quadrantal Bearing (QB) or Reduced Bearing System
Each system offers a unique approach to measuring and representing bearings, catering to various surveying needs and preferences.
Whole Circle Bearing System (WCB)
The Whole Circle Bearing (WCB) system, also known as the Azimuthal System, is a comprehensive method for measuring bearings. In this system:
- Measurement Basis: Bearings are measured clockwise from either the true north or true south direction.
- Range: The bearing values range from 0° to 360°, covering the entire circle around the point of reference.
- Tools: A prismatic compass is typically graduated using the WCB system, facilitating precise measurements in the field.
Illustration and Examples: Consider a survey line AB. In the WCB system, the bearing of AB (denoted as Q1) might be measured as 45°, indicating that line AB is oriented 45° clockwise from the north. Similarly, other lines like AC, AD, and AF would have bearings Q2, Q3, and Q4, respectively, each measured within the 0° to 360° range.
Quadrantal Bearing System (QB)
The Quadrantal Bearing (QB) system, also known as the Reduced Bearing System, simplifies bearing measurements by dividing the compass circle into four quadrants based on the cardinal directions.
- Measurement Basis: Bearings are measured from the nearest north or south direction, depending on which is closer to the line being measured. The measurement can be in a clockwise or counterclockwise direction.
- Range: Bearings in the QB system range from 0° to 90°, representing the angle within a specific quadrant.
- Quadrant Identification: Each bearing is associated with a quadrant designation, such as NE (Northeast), SE (Southeast), SW (Southwest), or NW (Northwest), indicating the general direction of the line.
Illustration and Examples: For instance, consider line AC lying in the Southeast quadrant. Its bearing is measured from the south direction, resulting in a bearing notation of “S B E,” where B represents the bearing angle measured clockwise from the south. If the bearing angle is 30°, it would be denoted as S30°E.
6. Conversion Between WCB and QB Systems
Surveyors often need to convert bearings between the Whole Circle Bearing (WCB) system and the Quadrantal Bearing (QB) system to suit different reporting or mapping requirements. The conversion process involves straightforward calculations:
- From WCB to QB:
- Identify the Quadrant: Determine which quadrant the bearing falls into based on the WCB value.
- Calculate the Angle: Subtract the nearest cardinal direction (0°, 90°, 180°, 270°) from the WCB value to obtain the QB angle.
- Assign Quadrant Designation: Based on the WCB value, assign the appropriate quadrant notation (NE, SE, SW, NW).
- From QB to WCB:
- Determine the Reference Direction: Identify whether the bearing is measured from north or south.
- Add/Subtract the QB Angle: Depending on the quadrant, add the QB angle to the reference direction to obtain the WCB value.
Example:
- Converting WCB of 135° to QB:
- 135° falls in the Southeast (SE) quadrant.
- QB angle = 135° – 90° = 45°
- QB notation = S45°E
- Converting QB of N30°W to WCB:
- N30°W indicates a Northwest (NW) quadrant.
- WCB = 360° – 30° = 330°
Understanding both systems and the conversion process is vital for surveyors to ensure flexibility and accuracy in various surveying contexts.
Conclusion
Bearings are indispensable in compass surveying, providing a reliable means to describe the direction of survey lines. The Whole Circle Bearing (WCB) system offers a complete 360° framework for precise directional measurements, while the Quadrantal Bearing (QB) system simplifies bearings into manageable 90° segments with quadrant designations. Mastery of both systems, along with the ability to convert between them, equips surveyors with the tools necessary for accurate and efficient fieldwork. As surveying techniques continue to evolve, a solid grasp of bearing systems remains foundational to the discipline, ensuring that surveyors can adapt to diverse challenges and maintain high standards of precision.