Reduced/Quadrantal Bearing in Surveying

Bearing refers to the process of determining the direction of a survey line in civil engineering surveying. The quadrantal bearing is a type of bearing notation. It is also known as the decreased bearing. Quadrantal bearing, as the name implies, is based on a line’s quadratic location.

What is Quadrantal Bearing or Reduced Bearing?

The horizontal angle formed by a line with the magnetic north or south (whichever is closer to the line) in the eastward or westward direction is known as the line’s Quadrantal Bearing or Reduced Bearing.

Both north and south are considered reference meridians in quadrantal or reduced bearing. Depending on the position of a survey line, the direction of the reference meridian to the line can be either clockwise or anticlockwise.

In order to represent the reduced bearing value of a line, the quadrant in which the line lies must be given.

So basically, Reduced Bearing (RB) is a method of measuring the bearing of a survey line in either a clockwise or anti-clockwise orientation from either the north or south direction closest to the line.

The reduced bearing system is also known as the Quadrantal Bearing System. The quadrantal bearing of a line, as the name implies, is always dependent on the quadrant in which the line lies.

What exactly is Bearing?

Bearing is as basic as the orientation of survey lines with respect to a meridian. Meridian is a constant reference line.

There are two types of bearing systems: whole circle bearing and reduced bearing. We have the ability to transition from one system to another.

Meridian Types

True Meridian: A line that runs through the true north and south poles and remains constant throughout. Astronomical observations are required to determine this line. Real bearings are bearings with respect to the true meridian.

Magnetic Meridian: The direction indicated by a freely suspended magnetic needle, and this magnetic N-S line fluctuates with place and time as it is impacted by the magnetism of the Earth. Magnetic bearing refers to bearing with regard to the magnetic meridian.

Arbitrary Meridian:  A well-defined reference object, such as a tower, whose position will not change; directions are measured with regard to it and are referred to as arbitrary bearings.

Reduced Bearing (RB) / Quadrantal Bearing (QB) Overview

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

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

In order to express the reduced bearing value of a line, the quadrant (or direction such as North-East, North-West, South-East, and South-West) in which the line lies must be specified.

Characteristics of reduced bearing

They include:

• Angles range from 0 degrees to 90 degrees.
• It is measured clockwise/anticlockwise from north/south (If the line is closer to the south and heading west, it is read as S ° W).
• Four quadrants are possible: NE, SE, SW, and NW.
• The RB system is utilized in surveyor’s compass.

The nature of reduced bearing in quadrants

This bearing system is completely dependent on the quadrant in which the line is located.

• If the survey line is in the first quadrant, its bearing would be 0 to 90 degrees NE.
• If the survey line is in the second quadrant, its bearing would be 0 to 90 degrees SE.
• If the survey line is in the third quadrant, its bearing would be 0 to 90 degrees SW.
• If the survey line is in the fourth quadrant, its bearing would be 0 to 90 degrees NW.

Difference between whole circle and reduced bearing

In surveying, two types of bearing measurements are used: whole circle bearing and quadrantal bearing (reduced bearing).

A surveyor must understand the distinctions between these two forms of bearing measurement in order to choose between them.

The primary distinctions between Whole Circle Bearing and Quadrantal Bearing (Reduced Bearing) are listed below.

1. In Whole Circle Bearing, the horizontal angle formed by a line with the magnetic north in a clockwise direction is the line’s whole circle bearing.

In Quadrantal Bearing/Reduced Bearing, the horizontal angle formed by a line with the magnetic north or south (whichever is closer to the line) in an eastward or westward direction is the line’s Quadrantal Bearing or Reduced Bearing.

1. In Whole Circle Bearing, only the magnetic north line is treated as a reference line, whereas in Quadrantal Bearing/Reduced Bearing, both the magnetic north and south lines are used as reference lines.
2. In Whole Circle Bearing, only the clockwise angle from the reference line is measured, whereas in Quadrantal Bearing/Reduced Bearing, both the clockwise and anticlockwise angles are measured.
3. In Whole Circle Bearing, the value of the whole circle bearing ranges from 0 to 360°, whereas in Quadrantal Bearing/Reduced Bearing, the value of the reduced bearing ranges from 0 to 90°.
4. Whole Circle Bearing Examples: 26°, 121°, 245°, 350°, and so on, whereas Quadrantal Bearing/Reduced Bearing Examples: N26°E, S59°E, S65°W, N10°W, and so on.

A Quadrantal Bearing Exemplification

You can take both the clockwise and anticlockwise angle from the reference line in the quadrantal bearing scheme.

It is required to specify which quadrant that line is located in. The quadrant is symbolized by the letters N (north), S (south), E (east), and W (west).

The surveyor’s compass detects a decrease in bearing.

The quadrants are shown below.

• N – E in the first quadrant
• S – E in the second quadrant
• S – W in the third quadrant
• N – W in the fourth quadrant

The following is an illustration of a quadrantal bearing.

N35° E, S49° E, N65° W, S25° W, and so forth.

Reduced bearing benefits

The advantages include:

1. The reduced bearing is a simple, economical system that can be used by all people regardless of their skills or knowledge.
2. It is easy to use and does not require any particular skill or knowledge in order to use it.
3. Reduced bearing is comparatively easier for surveyors to calculate than whole circle bearings and more popular among surveyors who want to review their surveying job results with a glance of the eyes only.
4. If a surveyor changes his position, it is easy to know exactly how the bearing has changed without having to repoint the instrument. This makes changes in bearing easier and quicker to apply than using whole circle bearings.
5. Reduced bearings are more precise and are more accurate than whole circle bearings, especially when dealing with angles less than 120 degrees.
6. Reduced bearings are easiest to obtain because they are the clockwise or anticlockwise angle from the nearest magnetic north or south line.
7. Moreover, because of its advantage of simplicity for both calculation and use by surveyors, reduced bearing is generally easier to understand than whole circle bearings, even though it is more complicated mathematically.
8. It is the preferred method of calculation in differentiating lines and determining their location with a compass.

Drawbacks of reduced bearing

They include;

1. Reduced bearings are more complicated mathematically than whole circle bearings and therefore require more time for calculation.
2. Reduced bearings are not applicable to the determination of North-South lines, so it can only be used to measure east-west lines. Whole circle bearing is required in order to determine north-south lines.
3. The measurement of the reduced bearing is more difficult than the measurement of the whole circle bearing because it requires an additional action, namely, measuring both clockwise and anticlockwise angles from the reference line in an eastward or westward direction.
4. The reduced bearing is unsuitable for large distances and high altitudes because it is not based on the magnetic meridian that crosses the whole earth.
5. Because of its calculation procedure, reduced bearings require more labor than whole circle bearings.
6. Because of its simplicity and comprehensibility, surveyors generally prefer whole circle bearings to reduced bearings.

FAQs

What is Reduced/Quadrantal Bearing in Surveying?

The horizontal angle formed by a line with the magnetic north or south (whichever is closer to the line) in the eastward or westward direction is known as the line’s Quadrantal Bearing or Reduced Bearing.

Reduced Bearing (RB) measures the bearing of a survey line in either a clockwise or anti-clockwise direction from either the north or south direction closest to the line.

What is the difference between whole circle and reduced bearing?

Whole circle bearing is determined by the magnetic meridian, which crosses the whole earth. Reduced bearing is determined by both the magnetic meridian and the line’s quadrant direction.

What is quadrantal bearing?

It is the horizontal angle formed by a line with the magnetic north or south (whichever is closest to the line) in an eastward or westward direction.

How would a surveyor measure reduced bearing on the ground?

Surveyors use a compass and nothing else to measure reduced bearings. In case of measuring bearings greater than 90 degrees, for instance, 126 degrees, the surveyor uses an instrument known as a protractor.

What is back bearing and reduced bearing?

Bearings measured in the survey’s progress direction are known as fore bearings, whereas bearings measured in the opposite direction of the survey are known as back bearings. A line’s bearing is the direction it takes with regard to a specific meridian; a meridian is a fixed reference line.

What is meridian in surveying?

Meridians are imaginary lines of longitude that go from the North Pole to the South Pole. A major meridian is a reference line that is used to survey a vast area. It was established as a straight line flowing north from the junction of the Ohio and Mississippi Rivers.

What is the difference between a surveyor’s compass and protractor?

The protractor is used to measure the bearing of a line during the survey; it is similar to a pair of compasses. A surveyor’s compass measures only the direction of magnetic north or south. Compass bearings are determined by using both the magnetic meridian and the line’s quadrantal bearing.

What is circle of bearings?

Circle of bearings is a circle formed by several reference lines representing quadrants on either side of a surveyed line. It is a device used in triangulation.

What is compass bearing?

Compass bearings are measured by both the magnetic meridian and the line’s quadrantal bearing. The compass is used to measure the direction of the quadrantal bearing.

It is obtained by using both the magnetic meridian and the line’s quadrantal bearing in a clockwise or anticlockwise direction, respectively, from either north or south.

What is azimuth in survey?

Azimuths are horizontal angles measured in the clockwise direction from the reference meridian. Azimuths are sometimes referred to as a whole circle bearing system (W.C.B). Azimuths are commonly employed in compass surveying and plane surveying, where they are measured from the north.

Which is the best definition of the meridian?

Any imaginary semicircle on the earth’s surface extending from the north pole to the south pole. or alternatively: A representation of a meridian on a map or globe that is numbered according to degrees of longitude.

What is true bearing and magnetic bearing?

True bearing and magnetic bearing are terms used in geography to refer to true north and magnetic north, respectively. The direction pointing to the North Pole is known as true north. True north is depicted on a map by meridians or lines of longitude.

Magnetic north, on the other hand, is the direction that points to the magnetic pole.

What is the formula of true bearing?

True Bearing = (Magnetic Bearing + Declination) = (89°45 + 5°30) = 95°15

What is bearing angle?

A bearing is the angle in degrees measured clockwise from north in mathematics. Bearings are often specified as a three-figure bearing. 30° clockwise from north, for example, is generally written as 030°.

What is FB and BB in surveying?

Bearings measured in the survey’s progress direction are known as fore bearings, whereas bearings measured in the opposite direction of the survey are known as back bearings.

What is forward bearing?

The bearing of the line in the forward direction of surveying is referred to as the fore bearing. The formula for calculating the progressive line’s fore bearing is F.B = B.B 180° + sign when B.B is less than 180° and − sign when B.B is greater than 180°.

What is relative bearing?

The angle between the forward direction of the ship and the location of another object is referred to as relative bearing. An object relative bearing of 0 degrees, for example, would be dead ahead; an object relative bearing of 180 degrees would be behind.

What exactly is whole circle bearing?

Whole circle bearing (WCB) is defined as the bearing of a line at any point measured with regard to the Meridian. The values for Whole Circle bearings range from 0° to 360°. In the Prismatic compass, the Whole circle bearing is commonly utilized.

What is grid bearing?

A horizontal angle measured clockwise with reference to grid north that expresses the direction of an object from a point.

What is square bearing?

Square bore ball bearings are specialized products that have all of the properties of normal Single Row Ball Bearings except that the inner ring has a square interior built for a square shaft rather than a round shaft. These items are also commonly measured in inches rather than metric measurements.