Whole Circle Bearing to Reduced Bearing (WCB to RB) | Surveying

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.
 

Bearing system is of two types - Whole circle bearing and reduced bearing. We can convert from one system to another. 

Whole Circle Bearing (WCB) / Azimuthal System

Bearings are measured clockwise from north of reference meridian

  • 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 used WCB system

Reduced Bearing (RB) / Quadrantal Bearing (QB)

Bearings are measured either clockwise/anti-clockwise from north/south whichever is close to the line.

  • 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

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 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

Few more examples for each quadrant to convert WCB to RB

  • WCB = 35° => First quadrant (NE) => Angle = 35° => RB = N35°E

  • WCB = 130° => Second quadrant (SE) => Angle = 180 - 130° => RB = S50°E

  • WCB = 240° => Third quadrant (SW) => Angle = 240° - 180° = 60° => RB = S60°W

  • WCB = 290° => Fourth quadrant (NW) => Angle = 360° - 290° => RB = N70°W

Try this! Convert ​S89°W to WCB

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