Triangulation: Measuring Distances and Angles for Surveying and Mapping, Study notes of Geography

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Introduction-Triangulation

Dr Moonis Zaheer

Geodetic Surveying

• Geodetic Surveying: Surveying technique to determine relative positions of widely spaced points, lengths, and directions which require the consideration of the size and shape of the earth. (Takes the earth’s curvature into account.)
• Geodetic survey is used to provide control points to which small surveys can be connected.

• Use to established a horizontal control system for a country
• The process of a measuring system comprised of connected triangles whose vertices are stations marked on the surface of the earth and in which angular observations are supported by occasional distance and astronomical observation is known as triangulation Triangulation

• Entire area to be surveyed is converted into framework of triangles
• If the length and bearing of one side and three angles of a triangle are measured precisely, the lengths and directions of other two sides can be computed
• Precisely measured line is called base line
• Computed two lines are used as base lines for two interconnected triangles
• Vertices of the individual triangles are known as triangulation stations
• Extending this process network of triangles can be computed over the entire area
• As a check the length of one side of last triangle is also measured and compared with the computed one Principle of Triangulation

• Subsidiary bases are measured at suitable intervals to minimize accumulation of errors in lengths
• Astronomical observations are made at intermediate stations to control the error in azimuth
• Those triangulation stations are called Laplace Stations. Principle of Triangulation

Purpose of Triangulation

• To establish the accurate control points for plane and geodetic surveys of large areas
• To establish the accurate control points for photogrammetric surveys
• Accurate location of engineering works

Primary Triangulation

• Highest grade of triangulation system
• To determine the shape and size of the earth's surface
• Stations are generally selected 16 km to 150 km apart Specifications: - Length of the base lines - 8 km to 12 km - Length of the sides - 16 km to 150 km - Average triangular error - less than 1" - Actual error of the base - 1: - Discrepancy between two measurements – 5 mm 𝐾𝑚

Secondary Triangulation

• To connect two primary triangulations to provide control points closer together than those of primary triangulation
• For the densification of horizontal control net work Specifications: - Length of the base lines - 2 km to 5 km - Length of the sides - 10 km to 25 km - Average triangular error - less than 3" - Actual error of the base - 1: - Discrepancy between two measurements – 10 mm 𝑘𝑚

Layout of Triangulation

• The arrangement of the various triangles of a triangulation series, is known as the layout of triangulation
• Three types of layout (1) Simple triangles in chain (2) Braced quadrilaterals in chain (3) Centred triangles and polygons

Simple triangles in chain

• Used when control points are provided in a narrow strip of terrain such as a valley between two ridges.
• Rapid and economical due to its simplicity of sighting.
• Not provide any check on the accuracy of observations as there is only one route through which distances can be computed. - check base lines and astronomical observations for azimuth at frequent intervals are very essential to avoid excessive accumulated error

Centred Triangles and Polygons

• Consists of figures containing centered polygons and centered triangles
• Used when vast area extending in all direction is required to be covered.
• The centered figures generally are quadrilaterals, pentagons, or hexagons with central stations.
• Provides proper check on the accuracy of the work
• low progress of the work due to more settings of the instrument

Factors to be consider in selecting a figure

• Simple triangles should be preferably equilateral
• Braced quadrilaterals should be preferably squares
• Centered polygons should be regular
• No angle of the figure, opposite a known side should be small
• The angles of simple triangles should not be less than 45°
• In case of quadrilaterals no angle should be less than 30°.
• In case of centered polygons, no angle should be less than 40°
• The sides of the figures should be of comparable length

Grid iron system

• Primary triangulation is laid in series of chains of triangles
• Usually run roughly along the meridians (north-south) and along the perpendiculars to the meridians (east- west) throughout the country
• Distance between two chains may vary from 150 km to 250 km
• Area between the parallel and perpendicular series of primary triangulation are covered by the secondary and tertiary triangulation systems.
• Adopted in India, Austria, Spain and France

Centered system

• Whole area of the survey is covered by a net work of primary triangulation extending outwards in all directions from the initial base line
• Base line is generally laid at the centre of the country
• Used for the survey of an area of moderate extent
• Adopted in United Kingdom