The directions of survey lines are fundamental to accurate mapping and can be defined in two primary ways:
- Relative to Each Other: In this method, directions are expressed in terms of the angles between two consecutive lines. This approach is useful for local surveys where the relationship between adjacent lines is more important than their absolute orientation.
- Relative to a Reference Direction: This method expresses directions in terms of bearings, which relate each line to a fixed reference direction. This approach is essential for larger surveys and for integrating local surveys into broader geographic contexts
Bearing
The bearing of a survey line is the horizontal angle between the reference meridian and the survey line, measured clockwise from the meridian. Bearings are typically expressed in degrees, minutes, and seconds, and are classified into four quadrants:
- Northeast (NE): 0° to 90°
- Southeast (SE): 90° to 180°
- Southwest (SW): 180° to 270°
- Northwest (NW): 270° to 360°
For example, a bearing of N 45° E indicates a line oriented 45 degrees east of north.
Meridian
A meridian is a fixed reference direction on the Earth’s surface, relative to which the bearings of survey lines are expressed.( A meridian is a fixed direction on the surface of the Earth, serving as a reference for expressing the bearings of survey lines.) There are several types of meridians used in surveying:
a) True (Geographic) Meridian
b) Magnetic Meridian
c) Arbitrary Meridian
d) Grid Meridian
Types of Meridian
A) True Meridian
A true meridian, also known as a geographical meridian, is a fundamental concept in geodesy and surveying. It is defined as the line of intersection between the Earth’s surface and a plane containing the North Pole, South Pole, and the observer’s position. This line represents the true north-south direction at any given location on Earth
Key characteristics of true meridians:
- Non-parallel nature: Geographical meridians at different locations are not parallel to each other. They converge at the poles, forming a network that resembles segments of an orange.
- Global reference system: The Earth’s equatorial circumference is divided into 360 degrees. The Prime Meridian, passing through Greenwich, England, is internationally recognized as 0°. Meridians east of Greenwich are designated as “East” and those west as “West.”
- Determination method: Precise determination of a true meridian at any location involves astronomical observations of celestial bodies, primarily the sun and stars.
- Stability: The true meridian at any given location remains constant over time, making it a reliable reference for long-term surveying projects.
- Applications: True meridians are particularly useful in engineering surveys to efficiently establish surveying lines during construction projects.
- Large-scale surveys: Due to the convergence of true meridians, they are most suitable for large-scale surveys covering limited areas.
- Official mapping: National survey departments, such as the Survey of India, typically base their official maps on true meridians.
Convergence of True Meridians
The non-parallel nature of true meridians leads to a phenomenon known as convergence. This convergence is more pronounced at higher latitudes compared to regions near the equator. The convergence angle between two meridians can be calculated using the following formula:
Convergence (in seconds) = Difference in longitudes (in seconds) × sin(latitude)
Where latitude (λ) is the latitude of the location.
Determination of True Meridian
A practical method for determining the true meridian at a given location involves observing the sun’s shadow:
- On level ground, draw a circle with a central point O.
- Place a vertical rod at O.
- Mark point B where the tip of the rod’s shadow first touches the circle’s circumference in the morning.
- Mark point C where the shadow tip touches the circle again in the afternoon.
- The line bisecting angle BOC represents the true meridian at O.
True Bearing and Azimuth
True Bearing: The horizontal angle between the true meridian and a survey line, measured clockwise, is called the true bearing of the line.
Azimuth: The smaller angle that a survey line makes with the true meridian. Unlike true bearing, azimuth does not specify the direction of measurement.
Calculation of Azimuth:
- If the true bearing is greater than 180°, subtract it from 360° to get the azimuth.
- If the true bearing is less than 180°, the azimuth equals the true bearing.
Note: In some countries, azimuth is measured from the south instead of the north.
B) Magnetic Meridian
The magnetic meridian is an imaginary line connecting the magnetic north and south poles at any given point on the Earth’s surface. It is visualized by the longitudinal axis of a freely suspended and properly balanced magnetic needle, unaffected by local attractive forces. The magnetic meridian rarely coincides with the true (geographic) meridian. The angular difference between these two is known as magnetic declination or variation. The position of the magnetic meridian is not fixed and undergoes both temporal and spatial variations due to changes in the Earth’s magnetic field.
Magnetic Bearing
Magnetic bearing is the horizontal angle formed between a survey line or direction of travel and the magnetic meridian at a given location. It is typically measured clockwise from magnetic north, ranging from 0° to 360°. Magnetic bearings are usually determined using a compass or other magnetic sensing devices. Like the magnetic meridian, magnetic bearings are not constant and are subject to change over time due to:
a) Diurnal variations (daily fluctuations)
b) Secular variations (long-term changes over years)
c) Magnetic storms and other geomagnetic disturbances
C) Grid Meridian
- Definition: A grid meridian is an artificial north-south line on a map, part of a rectangular coordinate system superimposed on the Earth’s curved surface.
- Purpose: Grid meridians simplify map reading, distance calculations, and location referencing within a specific geographic area.
- Relationship to true meridian: Grid meridians are typically parallel to a chosen central meridian within a defined zone, but not necessarily parallel to true north except at the central meridian.
Grid System Structure
- Zoning: Countries often divide their territory into multiple grid zones to minimize distortion.
- Central meridian: Each zone has a designated central meridian, usually a true meridian chosen for its central location within the zone.
- Boundaries: Zones are typically defined by specific lines of longitude and latitude.
- Grid lines: North-south grid lines are parallel to the central meridian, while east-west lines are perpendicular to it.
Grid Bearing
Grid bearings provide a practical way to express directions on grid-based maps:
- Definition: The horizontal angle between a line and the grid north, measured clockwise from grid north.
- Usage: Widely used in surveying, military operations, and civil engineering within a specific grid system.
- Advantage: Grid bearings remain constant along a straight line on the map, unlike true or magnetic bearings.
Grid Convergence
Grid convergence is a crucial concept for understanding the relationship between grid and true directions:
- Definition: The angular difference between grid north and true north at any given point.
- Variation: Grid convergence changes across a map sheet, being zero along the central meridian and increasing towards the zone edges.
- Direction: Described as east or west, indicating which way the grid north is offset from true north.
- Calculation: Grid convergence can be computed based on the location’s coordinates within the grid system.
D) Arbitrary Meridian
An arbitrary meridian is a practical solution for local surveys and small-scale mapping projects. It offers simplicity and consistency for specific survey tasks.
An arbitrary meridian is a chosen direction that serves as a reference line for measuring bearings in a survey, typically for small land plots or localized projects.
Unlike true, magnetic, or grid meridians, an arbitrary meridian is not tied to any global or standardized system.
Characteristics of Arbitrary Meridian
- Flexibility: Can be established in any convenient direction suitable for the survey area.
- Consistency: Provides a stable reference within the scope of a particular project.
- Simplicity: Eliminates the need to account for magnetic variations or grid convergence in local surveys.
Advantages of arbitrary meridian
- Invariability: Once established, it remains constant throughout the survey period.
- Easy recovery: Its direction can be easily re-established in future surveys of the same area.
- Local relevance: Well-suited for projects where global orientation is not critical.
- Reduced complexity: Simplifies calculations and reduces potential errors in small-scale surveys.
Establishing an Arbitrary Meridian
- Often aligned with a prominent local feature (e.g., a boundary line, building edge, or road).
- May be set perpendicular or parallel to a key survey line.
- Can be marked physically on the ground or defined by coordinates of two points.
