TRIANGULATION The horizontal positions of points is a network developed to
provide accurate control for topographic mapping charting lakes rivers and ocean coast lines and for the surve!s re"uired for the design and construction of pu#lic and private works of large e$tent% The horizontal positions of the points can #e o#tained in a
num#er of different wa!s in addition to traversing%
The method of surve!ing called triangulation is #ased on the
trigonometric proposition that if one side and two angles of a triangle are known the remaining sides can #e computed%
U&'& O( TRIANGULATION &UR)'* The triangulation surve!s are carried out +i, to esta#lish accurate control for plane and geodetic surve!s of large areas #! terrestrial methods% +ii, to esta#lish accurate control for photogrammetric surve!s of large areas% +iii, to assist in the determination of the size and shape of the earth #! making o#servations for latitude longitude and gravit!%
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+iv, to determine accurate locations of points in engineering works such as +a, (i$ing (i$ing centre line and a#utme a#utments nts of long long #ridges #ridges over large large rivers% +#, (i$ing centre line terminal points and shafts for long tunnels% +c, Transferring Transferring the control points across wide sea channels large water #odies etc% +d, .etection of crustal movements etc% +e, (inding the direction of the movement of clouds
/LA&&I(I/ATION O( TRIANGULATION &*&T'0 Triangulation surve!s are classified as first1order or primar! second1order or secondar! and third1order or tertiar!% •
ARRANG0'NT O( TRIANGL'& The #asic figures used in triangulation networks are the triangle
#raced or geodetic "uadrilateral and the pol!gon with a central station% The triangles in a triangulation s!stem can #e arranged in a num#er
of wa!s% &ome of the commonl! used arrangements also called la!outs are as follows 2% &ingle chain of triangles 3% .ou#le chain of triangles 4% 5raced "uadrilaterals 6% /entered triangles and pol!gons 7% A com#ination of a#ove s!stems%
5asic Triangulation figures
&ingle chain of triangles 8hen the control points are re"uired to #e esta#lished in a
narrow strip of terrain such as a valle! #etween ridges a la!out consisting of single chain of triangles is generall! used%
.ou#le chain of triangles •
A la!out of dou#le chain of triangles is shown in (ig% This arrangement is used for covering the larger width of a #elt% This s!stem also has disadvantages of single chain of triangles s!stem
5raced 9uadrilaterals A triangulation s!stem consisting of figures containing four corner
stations and o#served diagonals shown in (ig is known as a la!out of #raced "uadrilaterals% This s!stem is treated to #e the strongest and the #est arrangement
of triangles and it provides a means of computing the lengths of the sides using different com#inations of sides and angles%
/entered triangles and pol!gons This la!out in a triangulation s!stem is generall! used when vast
area in all directions is re"uired to #e covered% Though this s!stem provides checks on the accurac! of the work
generall! it is not as strong as the #raced "uadrilateral arrangement%
A com#ination of all a#ove s!stems &ometimes a com#ination of a#ove s!stems ma! #e used which
ma! #e according to the shape of the area and the accurac! re"uirements%
ROUTIN' O( TRIANGULATION &UR)'* The routine of triangulation surve! #roadl! consists of
+a,field work and +#, Office work The field work of triangulation is divided into the following operations +i, Reconnaissance +ii, 'rection of signals and towers +iii, 0easurement of #ase line +iv, 0easurement of horizontal angles +v, 0easurement of vertical angles +vi, Astronomical o#servations to determine the azimuth of the lines%
The field work of triangulation is divided into the following operations a, Ad:ustment of o#served Angles #, /omputation of lengths of the sides c, /omputations of latitudes departures and azimuths of all the sides% d, /omputation of independent coordinates%
R'/ONNAI&&AN/' It includes the following operations2% '$amination of terrain to #e surve!ed% 3% &election of suita#le sites for measurement of #ase lines% 4% &election of suita#le positions for triangulation stations% 6% .etermination of inter visi#ilit! of triangulation stations% 7% &election of conspicuous well1defined natural points to #e used as intersected points% ;% /ollection of miscellaneous information regarding+a, Access to various triangulation stations +#, Transport facilities +c, Availa#ilit! of food water etc% +d, Availa#ilit! of la#our +e, /amping ground%
(or reconnaissance the following instruments are generall! emplo!ed2% &mall theodolite and se$tant for measurement of angles% 3%
% .rawing instruments and material% ?% Gu!ed ladders creepers ropes etc% for clim#ing trees%
'rection of signals and towersA signal is a device erected to define the e$act position of a
triangulation station so that it can #e o#served from other stations whereas a tower is a structure over a station to support the instrument and the o#server and is provided when the station or the signal or #oth are to #e elevated%
&election of Triangulation &tations 2% Triangulation stations should #e inter visi#le% (or this purpose the station points should #e on the highest ground such as hill tops house tops etc% 3% &tations should #e easil! accessi#le with instruments% 4% &tation should form well1conditioned triangles% 6% &tations should #e so located that the lengths of sights are neither too small nor too long% &mall sights cause errors of #isection and centering% Long sights too cause direction error as the signals #ecome too indistinct for accurate #isection%
7% &tations should #e at commanding positions so as to serve as control for su#sidiar! triangulation and for possi#le e$tension of the main triangulation scheme% ;% &tations should #e useful for providing intersected points and also for detail surve!% >% In wooded countr! the stations should #e selected such that the cost of clearing and cutting and #uilding towers is minimum% ?% Grazing line of sights should #e avoided and no line of sight should pass over the industrial areas to avoid irregular atmospheric refraction%
0arking of Triangular &tations +i, The station should #e marked on perfectl! sta#le foundation or rock% The station mark on a large size rock is generall! preferred so that the theodolite and o#server can stand on it%% +ii, If no rock is availa#le a large stone is em#eded a#out 2 m deep into the ground with a circle and dot cut on it% +iii, A G%I% pipe of a#out 37 cm diameter driven verticall! into ground up to a depth of one metre also served as a good station mark%
+iv, Three reference marks at some distances on fairl! permanent features should #e esta#lished to locate the station mark if it is distur#ed or removed% +v, &urrounding the station mark a platform 4 m @ 4 m @ %7 m should #e #uilt up of earth%
&IGNAL& &ignals are centered verticall! over the station mark and the
o#servations are made to these signals from other stations% The accurac! of triangulation is entirel! dependent on the degree
of accurac! of centering the signals%
A signal should fulfil the following re"uirements +i, It should #e conspicuous and clearl! visi#le against an! #ackground% To make the signal conspicuous it should #e kept at least >7 cm a#ove the station mark% +ii, It should #e capa#le of #eing accuratel! centered over the station mark% +iii, It should #e suita#le for accurate #isection from other stations% +iv, It should #e free from phase or should e$hi#it little phase
/lassification of signals The signals ma! #e classified as under +i, Non1luminous opa"ue or da!light signals +ii, Luminous signals%
+i, Non1luminous signals Non1luminous signals are used during da! time and for short distances% These are of various t!pes% +a,
+c, ,- A pile of stone heaped in a conical shape a#out 4 m high with a cross shape signal erected over the stone heap is stone cairn%
5eacons +(ig% 2%3?,- It consists of red and white cloth tied round the three straight poles% The #eacon can easil! #e centered over the station mark%
+ii, Luminous signalsLuminous signals ma! #e classified into two t!pes +i, &un signals +ii, Night signals% +a, &un signals +(ig% 2%3B,- &un signals reflect the ra!s of the sun towards the station of o#servation and are also known as heliotropes% +#, Night signals- 8hen the o#servations are re"uired to #e made at night the night signals of following t!pes ma! #e used% 2% )arious forms of oil lamps with para#olic reflectors for sights less than ? km% 3% Acet!lene lamp designed #! /apt% 0c/aw for sights more than ? km% 4% 0agnesium lamp with para#olic reflectors for long sights%
TO8'R& A tower is erected at the triangulation station when the station or
the signal or #oth are to #e elevated to make the o#servations possi#le form other stations in case of pro#lem of inter visi#ilit!% The height of tower depends upon the character of the terrain
and the length of the sight% The towers generall! have two independent structures% The outer
structure is for supporting the o#server and the signal whereas the inner one is for supporting the instrument onl!%
5A&' LIN' The accurac! of an entire triangulation s!stem depends on that
attained in the measurement of the #ase line% The length of the #ase line depends upon the grade of the
triangulation% The #ase is connected to the triangulation s!stem through a #ase
net%
&election of site for #ase line 2% The site should #e fairl! level or gentl! undulating% If the ground is sloping the slope should #e uniform and gentle% 3% The site should #e free from o#structions throughout the length of the #ase line% 4% The ground should #e firm and smooth% 6% The two e$tremities of the #ase line should #e inter visi#le%
0easurement for #ase line Generall! the following t!pes of #ase measuring e"uipments are used 2% &tandardised tapes - These are used for measuring short #ases in plain grounds% 3% =unterCs short #ase- It is used for measuring ? m long #ase line and its e$tension is made #! su#tense method% 4% Tacheometric #ase measurements - It is used in undulating grounds for small #ases 6% 'lectronic distance measurement- This is used for fairl! long distances and has #een discussed in previous chapter%
&tandardised tapes (or measuring short #ases in plain areas standardised tapes are
generall! used% After having measured the length the correct length of the #ase
is calculated #! appl!ing the re"uired corrections%
=unterCs short #ase .r% =unter who was a .irector of &urve! of India designed an e"uipment to measure the #ase line which was named as =unterCs short #ase% •
It consists of four chains each of 33 !ards +3%22> m, linked together% There are 7 stands three1intermediate two1legged stands and two three1legged stands at ends % •
&AT'LLIT' &TATION &ome times it #ecomes difficult or impossi#le to set up the theodolite at a triangulation station% To secure well1conditioned triangles or to have good visi#ilit! O#:ects such as chimne!s church spires flag pole towers etc% Are selected as triangulation stations% &uch stations can #e sighted from other stations #ut instruments cannot #e set up at such stations for sighting other stations for measuring horizontal angles% In such cases a su#sidiar! station is selected near the main station as the instrument station% O#servations are taken to other stations from the su#sidiar! station% The su#sidiar! station is known as the satellite station false station or eccentric station% The method of appl!ing the correction due to eccentricit! of the satellite station is known as reduction to the centre% The distance #etween the triangulation station 5 and the &atellite station & is called the eccentric distance +d,% •
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