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Reduced Bearing (RB) / Quadrantal Bearing (QB) | Surveying

In Reduced Bearing (RB), the bearing of a survey line is measured either in a clockwise or anti-clockwise direction from either of the north or south direction whichever is close to the line.


The reduced bearing is also known as Quadrantal Bearing System. As its name indicates the quadrantal bearing if a line always depends upon the quadrant, in which the line lies.

Reduced Bearing (RB) / Quadrantal Bearing (QB)

The bearing system is of two types - Whole circle bearing and reduced bearing. First, let us understand what is meant by bearing and meridians.


What is Bearing?

Bearing is as simple as the direction of survey lines w.r.t. a meridian.


Meridian is a fixed reference line.


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


Types of meridian

  • True Meridian: Line through true north and south poles, and this remains constant throughout. To find out this line, we need astronomical observations. Bearing with respect to true meridian is known as true bearings.

  • Magnetic Meridian - Direction indicated by a freely suspended magnetic needle, and this magnetic N-S line changes with location and time as they are affected by earth’s magnetism. Bearing with respect to magnetic meridian is known as the magnetic bearing.

  • Arbitrary Meridian - Well defined reference object like a tower whose position is not going to change, directions are measured with respect to it and they are known as arbitrary bearings

Reduced Bearing (RB) / Quadrantal Bearing (QB)


The horizontal angle made by a line with the magnetic north or south (whichever is nearer to the line) in the eastward or westward direction is the quadrantal Bearing or Reduced Bearing of the line.


In quadrantal bearing or reduced bearing system, both north and south are considered as reference meridians. Depending upon the position of a survey line, the direction of the reference meridian to the line can be either clockwise or anticlockwise.


In the expression of the reduced bearing value of a line, quadrant(or direction like North-East, North-West, South-East and South-West)has to be mentioned in which the line lies.​

Characteristics of reduced bearing

  • 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 the south and going towards west, it is read as S β° W)

  • Four quadrants are possible namely NE, SE, SW and NW.

  • RB system is used in Surveyor's compass.


Nature of reduced bearing in quadrants


This bearing system completely depends upon the quadrant on which the line lies.

  • If the survey line is there in 1st quadrant, then its bearing would be 0 to 90 degrees NE.

  • If the survey line is there in 2nd quadrant, then its bearing would be 0 to 90 degrees SE.

  • If the survey line is there in 3rd quadrant, then its bearing would be 0 to 90 degrees SW

  • If the survey line is there in 4th quadrant, then its bearing would be 0 to 90 degrees NW.

Solve this one!

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