Meridians and Bearings in Surveying

In surveying, meridians and bearings play crucial roles in determining and expressing directions between points. In order to grasp the concepts of meridians, bearings, and surveying, it is essential for you to comprehend this fundamental concept.

This article comprises the types of meridians and bearings that are used for surveying and geographical measurements.

What are Meridians in Surveying?

We know the fact that the Earth rotates around an axis that connects the North and South Poles. These poles are widely recognized as true north or geographical north and true south or geographical south. In the field of geography, we utilize a system of imaginary lines to define and understand different regions on the Earth's surface. These lines include latitudes, which extend horizontally from west to east, and longitudes or meridians, which extend vertically from the North Pole to the South Pole.

Meridians also called a line of longitude are imaginary lines that run from true north to true south poles along the earth’s surface as shown in the figure.

As shown in the figure, based on this definition, there are several longitudinal lines possible. As the earth is spherical (an oblate spheroid) the total angle is 360 degrees and hence the longitudinal lines are placed at a gap of 1 degree thus giving 360 longitudinal lines along the earth as shown. Hence, these longitudinal lines are measured from 0 degrees to 360 degrees.

Based on this introduction we will dive into the various types of meridians used in geographical and surveying studies, which includes:

1. Prime meridian
2. True meridian or geographical meridian
3. Magnetic meridian
4. Arbitrary meridian
5. Grid meridian

1. Prime Meridian or Greenwich Meridian Line

The prime meridian is an imaginary line that runs from the North Pole to the South Pole, dividing the Earth into the Eastern Hemisphere and the Western Hemisphere.

The prime meridian is established at a longitude of 0 degrees and acts as the starting point for measuring longitudes around the globe. Hence, there is only one prime meridian possible and the most widely recognized prime meridian is the one that passes through the Royal Observatory in Greenwich, London. This prime meridian, commonly referred to as the Greenwich Meridian, was internationally adopted in 1884 at the International Meridian Conference.

Prime Meridian provides a standard reference for cartographers, navigators, and scientists to accurately determine the geographic coordinates of any place on Earth.

2. True Meridian or Geographical Meridian

True meridian is the line of longitude that runs through Earth’s true north and true south. The true meridian at any point aligns with the Earth’s axis ( True North and South Pole).

Each point on the Earth's surface can have its own unique true meridian. As you move eastward or westward from the prime meridian (0 degrees), the longitude values of the true meridians will vary. For example, a location with a longitude of 45 degrees will have a true meridian that passes through that point and has a longitude of 45 degrees, as shown in the figure below.

True meridian is established by astronomical observations and is fixed. The directions measured with respect to the true meridian do not change as the true meridian is a fixed direction.
For most surveys, the true meridian is used, especially for demarcating property lines.

3.Magnetic Meridian

The magnetic meridian is an imaginary line that represents the direction of the Earth's magnetic field at a specific location. It is the reference line that passes through the magnetic north and magnetic south. Hence, it is a line that runs perpendicular to the surface of the Earth and passes through the point where a compass needle points to magnetic north.

In simple terms, the magnetic meridian indicates the direction in which a magnetic compass needle aligns itself in response to the Earth's magnetic field. The magnetic field of the Earth is not uniform and varies in strength and direction across different locations. The magnetic meridian is important in navigation and compass use because it provides a reference for determining directions relative to magnetic north. By aligning a compass needle with the magnetic meridian, one can establish the north-south axis and navigate using magnetic bearings.

It is important to note that the magnetic meridian is not the same as the true meridian, which represents the line of longitude passing through a specific location. The magnetic meridian and true meridian can differ due to the variation in magnetic declination, which is the angular difference between magnetic north and true north. The magnetic meridian and true meridian won't coincide with each other in place. The horizontal angle between these two meridians is known as the magnetic declination/declination angle.

As shown in the figure above, with location,  the meridians vary. This way infinite combinations of magnetic meridians are possible passing through their magnetic north and south. Magnetic meridians are represented in dotted lines. Similarly, an infinite combination of the true meridian passing through Nt and St is possible. The declination at point A is hence α and that at point B is β.

Read More On: Declination and Dip, Variations and Isogonic Chart

4. Arbitary Meridian

An arbitrary meridian refers to a selected line of longitude that is chosen for convenience or specific purposes, rather than being based on any established reference point or natural feature. It is a meridian that is not aligned with any significant geographic or magnetic marker.

Unlike the prime meridian, which is internationally recognized and established as the reference point for measuring longitudes, an arbitrary meridian can be any line of longitude that is designated for a particular project or local use. It is often chosen based on convenience, ease of measurement, or local requirements.

Arbitrary meridians are sometimes used in small-scale mapping or surveying projects that do not require global or standardized references. They can be established to facilitate regional or local measurements, where precise alignment with the prime meridian may not be necessary.

However, it is important to note that the use of arbitrary meridians can introduce challenges when attempting to integrate data or coordinates from different sources or regions. The lack of a universally recognized reference point can make it difficult to compare or align geographic information.

5. Grid Meridian

Grid meridians are lines that are part of a coordinate grid system used on maps or charts. In a grid-based coordinate system, a grid meridian is a chosen line of reference that runs parallel to the meridians of longitude on a map or grid. It is a constructed line that facilitates the measurement and plotting of coordinates on a grid system.

They are often represented as vertical lines on a map, intersecting with horizontal lines (parallels) to form a grid. Grid meridians are based on a specific projection or coordinate system used for the map. Unlike meridians, which converge towards the poles, grid meridians are typically straight and parallel, allowing for easier measurement and navigation.

Bearings in Surveying

In surveying, a bearing refers to the direction of a line measured in degrees, typically measured clockwise from a reference direction, such as north. Bearings are used to describe the orientation or alignment of lines, angles, or points in surveying. 

Bearings provide a standardized and precise method for describing directions in surveying, allowing surveyors to establish accurate measurements, alignments, and boundaries essential for various surveying applications.

Types of Bearings in Surveying

Bearings as mentioned before, is a system of designating the direction of lines. The bearings of lines can be measured with respect to any meridian. Based on the type of meridian that is employed, it can be:

1. True Bearing
2. Magnetic Bearing
3. Grid Bearing
4. Arbitrary Bearing

1. True Bearings

True bearing refers to the direction of a line measured in degrees clockwise from the true meridian. The true meridian represents the line of true north-south alignment on the Earth's surface. 

As a true meridian at a point is fixed, true bearings provide a fixed reference direction unaffected by magnetic variations. The use of the true meridian ensures accuracy and consistency in measuring and communicating directions in surveying, navigation, and mapping activities.

If you are using a true instrument like a theodolite or total station, the measured bearing is already a true bearing since these instruments directly measure angles relative to the true meridian. In this case, there is no need to apply any correction for magnetic declination.

2. Magnetic Bearings

Magnetic bearing refers to the direction of a line measured in degrees clockwise from the magnetic north (magnetic meridian). It is a type of bearing that is influenced by the Earth's magnetic field.

If you are using a magnetic instrument like a compass, the measured bearing will already be a magnetic bearing. Magnetic bearings are commonly used in surveying, navigation, and mapping, particularly when magnetic instruments such as compasses are employed.

As stated in the chapter on Dip and Declination in Surveying, the magnetic north deviates from the true north (true meridian) by an angle, which is called a declination. In the figure, TN represents the true north of the true meridian and MN represents the magnetic north. If the magnetic declination is on the left side of the true meridian, the angle formed between the two meridians is a declination west (-ve) and that formed on the right is called a declination east (+ve).

Dip and Declination Eastwards and Westwards

1. Declination is used to determine the true bearing
2. True bearing = Compass bearing + declination
3. If the declination is declination east, then it is added ( compass bearing + declination)
4. If the declination is declination west, then it is subtracted ( compass bearing - declination)

The magnetic north can vary based on the location and changes in the Earth's magnetic field over time. Therefore, it is important to account for magnetic declination, which is the angular difference between true north and magnetic north, when using magnetic bearings. Magnetic bearings are useful in areas where magnetic instruments are readily available and provide a convenient and practical method for determining directions.

3. Arbitrary Bearings

Arbitrary bearing refers to a type of bearing measured with respect to an arbitrary reference meridian. Unlike true bearings, which are measured from the true meridian, or magnetic bearings, which are measured from the magnetic meridian, arbitrary bearings are based on a chosen reference meridian that is convenient or specific to a particular surveying project.

The use of an arbitrary bearing may occur in situations where a specific reference meridian is selected for ease of measurement or for alignment purposes. It is important to note that arbitrary bearings do not have a fixed relationship to true north or magnetic north and are not influenced by magnetic declination.

As shown in the figure above, O and A are two points either defined on permanent strutcures or fixed by tie measurements with respect to points identifiable on permanent structure. Hence, here AO is the arbitrary meridian chosen. The angle θ1 is the arbitrary bearing of line AB with respect to AO. 

Arbitrary bearings are typically used in specific surveying applications where the chosen reference meridian is known and agreed upon by all parties involved. They provide a relative direction for surveying operations within the context of that specific project or survey.

4. Grid Bearings

Grid bearings refer to the direction of a line measured in degrees clockwise from a reference meridian in a specific map projection or grid system. They are commonly used in surveying when working with coordinate systems and mapping.

The grid line bearing of a line on a map can be either determined using a compass as shown in the figure below or through calculations.

In the below figure, if A and B are the starting and end point of the line and their coordinates are (n1,m1) and (n2,m2). 

If AB is measured from the grid line ON- called the grid line meridian and if θ is the grid line bearing, then:

In a grid-based survey or map, a grid network is established with horizontal and vertical lines forming a coordinate system. The grid lines are often parallel to the true meridian and are spaced uniformly. Grid bearings allow for a consistent and precise representation of directions within the grid system.

Grid bearings are useful in situations where accurate positioning and alignment on a map or within a coordinate system are essential. They provide a standardized method for measuring and communicating directions, ensuring that features and measurements on the map align accurately with real-world locations.

It is important to note that grid bearings are distinct from true bearings and magnetic bearings, as they are based on a specific map projection or grid system rather than the true or magnetic meridian.

Bearing Systems in Surveying

Bearings can be measured by two methods:

1. Whole-Circle Bearing (WCB) System or Azimuth
2. Quadrantal Bearing System (QB) or Reduced Bearing

1. Whole-Circle Bearing (WCB) System

The WCB system is a method of measuring bearings that uses a complete angle in a circle. In this system, bearings are measured from a reference north meridian and continue in a clockwise direction to form a full circle. This bearing is called as azimuth of a line. 

Whole circle bearing system (W.C.B) or Azimuthal System 

In the WCB system:

1. Bearings are measured from the North magnetic meridian.
2. Measured in the clockwise direction.
3. W.C.B of any line lies between 0 to 360 degrees
4. It is implemented in Prismatic Compass

In plane surveying, the azimuths are measured from the North.The National Geodetic Survey of the National Oceanic and Atmospheric Administration (NOAA) (formerly the United States Coast and Geodetic Survey) always uses south as the zero direction. In wildland fire service, the azimuth is always read from the north point.

2. Reduced Bearing or Quadrantal Bearing System (QB)

The QB system divides bearings into quadrants: North, East, South, and West. Bearings are measured with respect to the reference meridian within the respective quadrant. QBs are expressed as a combination of the quadrant and the angle within that quadrant.

Reduced Bearing

The reduced bearing is represented by the quadrant in which the line is present by letter N or S followed by the bearing value and East or West following it. For example, a line OA making an angle α in the first quadrant (NE) is given as N α E. This designation is called as quadrantal system of bearings.
 

Quadrantal Bearing System (Q.B) or Reduced Bearing

In the Q.B system:

1. Bearings can be measured either from North or south whichever is near.
2. Measured clockwise or anti-clockwise
3. The bearings obtained lie between 0 and 90 degrees
4. It is implemented in Surveyor's Compass

3. Back Bearings and Fore Bearing in Surveying

Fore Bearing

Fore bearing refers to the forward direction of a line measured from the starting point or the observer's position. It represents the angle measured in degrees from a reference meridian (such as true north or magnetic north) in a clockwise or counterclockwise direction. Fore bearings are typically measured and recorded during surveying operations to establish the direction of a line in relation to the reference meridian.

Back Bearing

Back bearing is the opposite direction of the fore bearing. It represents the reverse direction of a line, measured from the endpoint or the reverse observation point back toward the starting point. Back bearings are often calculated by adding or subtracting 180 degrees from the corresponding fore bearing. They provide a reference for retracing or reversing the line's path during surveying or navigation.

A bearing of a line AB measured from A to B is (α) called as fore bearing or forward bearing as shown in the figure below. If the bearing is measured in the reverse direction from B to A it is called as backward bearing or back bearing (α ')

Back Bearings and Fore Bearing in Surveying

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