# Triangulation

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Triangulation: Process of forming and measuring the triangles.  Triangulation is a type of surveying technique in which a region is divided into a series of triangular elements based on a line of known length known as Base Line. So that the accurate measurements of distances and directions (bearings) should be made by the application of trigonometric knowledge and rules.  Triangulation is a process of determining the location of a point by measuring the angles to it i.e. ending at it, initiated from the other known points located at a fixed Base Line rather than measuring the distances up to the point (under consideration) directly (which is known as Trilateration). This point is then fixed as a third point of the triangle with one known side and two known angles.  Triangulation is a system of establishing the horizontal control usually in Geodetic Surveying as it is based on trigonometric proposition that if one side and two angles of the triangles are known, the remaining sides can be computed. A triangulation system consists of a series of joined or overlapped triangles in which the length of one side is fixed and known and called Base Line. All the angles are usually measured from the vertices located on Base Line and sides are calculated from those angles. The vertices of individual triangles are the location of Triangulation Stations. Triangulation can also be referred to as: accurate surveying of group or system of very large triangles called Triangulation Network. This type of surveying was followed from the work of Willebrord Snell (a Dutch Mathematician; 1580 – 1626) who showed how a point could be located from the angles subtended from three known points but measured at a new unknown position i.e. point rather than the previously known points; a method called Re-sectioning.The triangulation surveying method uses the triangular figures to determine the survey data. Triangulation operations are not confined to one area at one time. Several operations are involved in triangulation surveying method. The triangulation surveying generally consists of:Field work and (b) ComputationsRe-Sectioning: It is determination of the location of a point in surveying, by sighting from or towards that unknown point towards or from two or more other points of known position. Re-sectioning method makes it possible to find the position of an unknown target by measuring its position relative to the two (or more) known stations

it is divided into the following operations (in sequence):(i) Reconnaissance (Reccy or Recce) (ii) Establishing the Signals And Towers(iii) Measurement of Base Line(iv) Measurement of Horizontal Angles(v) Measurement of Vertical Angles
Triangulation Surveying Error is minimized if a network of the triangles formed at the appropriate largest scale, is firstly established. Points inside the said triangles can then be accurately located with reference to their external network. As the bases (Base Line) are measured, each length-measuring person must record all the base measurements in a notebook. As soon as the practical finishes, these recorded distances are transferred into the Field Notes kept by the recorder (recording person). When the base-line is measured with an electronic equipment, the recorder should also record the distances from that equipment into the field notebook.
Basic Triangulation Figures:The triangles in a triangulation system can be arranged commonly used arrangements, also known as Layouts, are given as follows :Classification of Triangulation System:On the basis of extent or area of the survey and on the degree of accuracy, triangulation surveys are classified as: (a) Primary or First Order Triangulation (b) Secondary or Second Order Triangulation and (c) Tertiary or Third Order Triangulation.(a) Primary or First Order Triangulation: This method comprises and is used to cover an extremely vast area e.g. whole the country or province / state; shape and size of the earth surface or terrain with reference to the control networks / stations are required to determine. (b) Secondary or Second Order Triangulation: This system comprises a network of triangles situated in the First Order Triangulation system. It covers the area of a very vast area e.g. provinces / states included inside the area of the country, or area of the (political) divisions included inside the area of the province / state.(c) Tertiary or Third Order Triangulation: This system is smaller in area than the Secondary Triangulation system.It is used to develop the control points for the local development / local government, topographic and hydrographic surveys. It is also known as Topo-triangulation.
:1. Simple triangles should preferably be the approximate equilateral triangles.2. Braced quadrilaterals should preferably be the approximate squares.3. Centered polygons should preferably be the approximate regular polygons.4. The arrangement should be such that the computations can be done through two or more independent routes.5. The arrangement should be such that at least one route (preferably the two routes) should form the well-conditioned triangles.6. No angle of the figure, opposite to a known side should be kept small. 7. Angles of the simple triangles should not be less than 45° and in case of quadrilaterals, no angle should be less than 30°. 8. The sides of the figures should be of comparable lengths. Very long lines and very short lines should be avoided.9. The layout should be such that it should require least work to achieve maximum progress. It should be noted that if a very small angle of a triangle does not fall (falls) opposite to the known side, it does not affect (would affect) the accuracy of triangulation.
Layout of the Triangles: Triangles (to be) included in a triangulation system is laid out or arranged in the following ways: (i) Single Chain of Triangles(ii) Double Chain Triangles (iii) Braced Quadrilaterals (iv) Centred Triangles (v) Polygons (vi) Combination of the above ones.Single Chain of Triangles: It looks like the letter M or W-configuration drawn between the two parallel-like lines (every left side {forming the base of that triangle} enclosed between the said parallel lines acts as a Base Line for establishing the other two sides of the said triangle, for right-hand-side progressing chain of triangles).It is used to cover narrow strip of terrain. Rapid and economic but not so accurate. To maintain accuracy, Base Line is run frequently. Double Chain of Triangles: It looks like a chain of two up and down (or side by side) triangles enclosed between the two parallel-like lines; the third central line passes internally joining the interior vertices of the said triangles.It is used where the area is wider than the above-mentioned area.