Whole Circle Bearing to Reduced Bearing (WCB to RB) | Surveying
Updated: Jan 19
In Whole Circle Bearing - Bearings are measured clockwise from north of reference meridian; In Reduced Bearing - Bearings are measured either clockwise or anti-clockwise from north/south whichever is close to the line.
Let us see a few basic concepts before we jump on the conversion steps. If you already know them, skip directly to the WCB to RB conversion steps
What is bearing?
Bearing is as simple as the direction of survey lines w.r.t. a meridian.
Meridian is a fixed reference line.
Whole Circle Bearing (WCB)
Bearings are measured clockwise from north of reference meridian.
It is also known as the Azimuthal System
It varies from 0 degrees to 360 degrees in the clockwise direction
North will be zero degrees; East will be 90 degrees; South will be 180 degrees and West will be 270 degrees.
Prismatic compass uses the WCB system
Examples of WCB
Line from origin to A (OA) : The angle is measured from the north to OA represented by θ in the figure.
Line from origin to B (OB): The angle is measured from the north to OB represented by ϕ in the figure.
Reduced Bearing (RB)
Bearings are measured either clockwise/anti-clockwise from north/south whichever is close to the line.
It is also known as Quadrantal Bearing (QB)
Angles vary from 0 degrees to 90 degrees
It is measured from either clockwise/anti-clockwise from north/south (If the line is closer to south and going towards west, it is read as Sβ°W)
Four quadrants are possible namely NE, SE, SW and NW
Surveyor's compass used RB system
Examples of RB
Line from origin to A (OA) : The angle is measured from the north to OA because OA is closer to the north. It is represented by NαE in the figure.
Line from origin to B (OB): The angle is measured from the south to OB because OB is closed to the south. It is represented by SβW in the figure.
Conversion from Whole Circle Bearing to Reduced Bearing
It is very easy to convert if we draw diagrams as shown below.
In this example, WCB = 240°
It lies in the third quadrant as the angle is between 180° and 270°
So, the quadrant position reading as per RB is SW
The angle will be 240° - 180° = 60°
RB = S60°W