triangulation (muhammad salman's conflicted copy 2016-04-03)

8/17/2019 Triangulation (Muhammad Salman's Conflicted Copy 2016-04-03)

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TRIANGULATION


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TRIANGULATION

• It is one of the methods of providingcontrol in an area which is to besurveyed

• It is based on the Trigonometricproposition that if one side andthree angles of a Triangle be

known, the remaining sides canbe computed b the applicationof !in Rule i.e.


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TRIANGULATION

These stations form the vertices of a seriesof mutually connected triangles, thecomplete gure called as triangulation

sstem For checking, last line is measured

accurately on eld and compared with thecommutated from triangulation, called

check base Check bases are established regularly in

series of long triangulation system


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TRIANGULATION

The triangulation stations at whichazimuth, latitudes and longitudes aremeasured from astronomical

observations are called azimuth,latitude or longitude stations

Triangulation system is used to

establish control points with respectto distances from a reference point,longitudes or latitudes and azimuths


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TRIANGULATION The obect of triangulation is to determine the

relative position of a system of widely separatedpoints on the surface of earth and also theirabsolute positions.

The relati"e positions are determined in

terms of a#imuths and line $oining them,absolute position is determined in terms oflatitudes and longitudes and ele"ation abo"e%!L&

The geodetic points so determined will furnish themost precise controls for a more detailed survey ofthe intervening country


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Ob$ecti"e

The main objective of triangulation is to provide a number of stationswhose relative and absolute positions, horizontal as well as vertical,

are accurately established. More detailed location or engineering

survey are then carried out from these stations.

The triangulation surveys are carried out

(i)

(ii)

(iii

)

(iv)

to establish accurate control for plane and geodetic surveys of large areas,

to establish accurate control for photogrammetric surveys of large areas,

to assist in the determination of the size and shape of the earth by making observations for

latitude, longitude

to determine accurate locations of points in engineering works such as

(a) !i"ing centre line and abutments of long bridges over largerivers.

(b) !i"ing centre line, terminal points, and shafts for long tunnels.

(c) Transferring the control points across wide sea channels, large

water bodies, etc..

(d) !inding the direction of the movement of clouds.


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TRIANGULATION !ethods employed in "eodetic survey to

establish control are Triangulation # !ore accurate

$recise Traversing # %ess accurate but in areas

where Triangulation is not feasible e&g denselywooded country of very 'at ground


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A B

C

Base Line AB is measured

Internal angles at A, B , C are measured

D


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'rinciple

PRINCIPLE OF TRIANGULATION!igure shows two interconnected triangles ABC and BCD. #ll the angles in

both the triangles, and the length L of the side AB, have been

measured.#lso the azimuth ( of AB has been measured at the triangulation

station A, whose coordinates ( X A , Y

A), are known.

The objective is to determine the coordinates of the triangulation stations

B, C , and D by the method of triangulation. $et us first calculate the

lengths of all the lines.

%y sine rule in∆ ABC , we have


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'rinciple AB BC

= CA

&e havesin '

sin sin *

AB L = l AB

or BC = l BC

sin '

L sin

and CA = l CAsin '

L sin *

+ow the side BC being known in ∆ BCD, by sine rule, we have

sin

sin - sin

BC CD=

BD

&e have BC = l

BC sin '

L sin

or = l CDCD ? sin ' sin

L sin sin -

= l BDand BD ??sin ' sin

L sin sin


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'rinciple$et us now calculate the azimuths of all the lines.

#zimuth of AB θ = θ AB

#zimuth of AC θ + ∠ = θ AC

#zimuth of BC θ + /0° − ∠* = θ BC

#zimuth of BD θ + /0° − (∠* + ∠-) = θ BD

#zimuth of CD θ − ∠* + ∠ = θCD

!rom the known lengths of the sides and the azimuths, coordinates as below.

+orthing of AB l AB cos θ AB = L AB1eparture of AB l AB sin θ AB= D AB

+orthing of AC l AC cos θ AC = L AC 1eparture of AC l AC sin θ AC = D AC

+orthing of BD l BD cos θ BD = L BD

1eparture of BD l BD sin θ BD = L BD


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'rinciple

+orthing of CD l CD cos θCD = LCD

1eparture of CD l CD sin θCD = DCD

The desired coordinates of the triangulation stations B, C , and D are as follows

2.3 coordinate of B, X B

= X A + D AB

43 coordinate of B, Y B = Y A + L AB X 3coordinate

of C , X C

= X A+ D AC Y 3coordinate of C , Y C

= Y A+ L AC X 3coordinate of D, X D = X B +

D BD Y 3coordinate of D, Y D = Y B + L BD

5t would be found that the length of side can be computed more than once

following different routes, and therefore, to achieve a better accuracy, the


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T() 'RO*)!!a. )election of suitable points as triangulation

stations in the area to be surveyedb. !easurement of a *ase %ine

c. !easurement of all the angles of the triangle andadustment of misclosures

d. Computations of lengths of other two sides of thetriangle

e. Computation of coordinates of unknown pointf. Taking one computed side as *ase for the ne+t

triangle and measurement of all the angles and soon

g. !easurement of a Check *ase at an interval of ((to -(( m

h. /etermining 0zimuth at the intervals of -( m byastronomical observations. /etermining of%ongitude and latitude are also necessitated at

times


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TRIANGULATION +IGUR)!

a. Triangles

b. 1uadrilaterals

c. $entagon or 2e+agons

Chain of braced 3uadrilaterals is the bestfollowed by centered point polygon


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a. Triangles

b. 1uadrilaterals

c. $entagon or 2e+agons

Chain of braced 3uadrilateralsis the best followed by centered

point polygon


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a. )ingle Chained Triangles

b. /ouble Chain Triangles

c. *raced 1uadrilaterals


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d. Centered triangles and polygons


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TRIANGULATION +IGUR)!CRITERIA FOR SELECTION OF THE LAYOUT OF TRIANGLES

.6imple triangles should be preferably e7uilateral.*.%raced 7uadrilaterals should be preferably appro"imate s7uares.

'.8entered polygons should be regular.

-.The arrangement should be such that the computations can be done through two

or more independent routes.

.The arrangement should be such that at least one route, and preferably tworoutes form well3 conditioned triangles.

.+o angle of the figure, opposite a known side should be small, whichever end

of the series is used for computation.

9.#ngles of simple triangles should not be less than -:, and in the case of

7uadrilaterals, no angle should be less than '0:. 5n the case of centered

polygons, no angle should be less than -0:./.The sides of the figures should be of comparable lengths. ;ery long lines and

very short lines should be avoided.


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*LA!!I+I*ATION

a. $rimary

4. Initial survey of an area

. First order standard accuracy

5. 6ery $recise e3uipments and methodsemployed

7. %ength of base line -&( km or more andsides 5( to 48( km or more. %onger lengths

-. Triangle misclosure 49:59

8. /egree of accuracy is 4 in -((,(((

;. Check on base is 4 in -(((


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)!IGN ofTRIANGULATION

Types of frame work for $rimarytriangulation

a. )eries of connecting chains or "ridiron system.

b. 0 continuous mesh of triangles orthe central system


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*LA!!I+I*ATION

b. )econdary

4. *reakdown of primary triangle

. )econd order accuracy

5. %ess $recise e3uipments and methodsemployed as compared to $rimary

7. %ength of base line &- km and sides ? to ;(km.)horter lengths as compared to primary

-. Triangle misclosure & 59 to ?98. /egree of accuracy is 4 in -(,(((

;. Check on base is 4 in 4(,(((


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*LA!!I+I*ATION

c. Tertiary4. Further break down of primary and secondary

work to provide control for Topographic survey

. Third order accuracy

5. %ess $recise e3uipments and methods employedas compared to $rimary

7. %ength of base line 4&5 km and sides 4.- to 4(km. )maller triangles

-. Triangle misclosure & 89 to 498. /egree of accuracy is 4 in -(((

;. Check on base is 4 in -(((


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A-!OLUT) 'O!ITION,ORI)NTATION . !*AL)

a. 0ccurate measurement of *ase willset the scale

b. /etermining the 0zimuth will + theorientation

c. /etermining the %ongitude and%atitude of one of the baseterminals will + the position on theearth@s surface

o


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oA**URA*0

• 0ccuracy is preserved by

a. Check *ases at intervals of (( to -((mb. 0zimuth is checked at intervals of -(m

c. =sing well conditioned gures. 0ngle but ane3uilateral triangle is ideal and s3uare e3uilateral is ideal

d. Fully observing all closed gures

1 The accuracy of a triangulation system is greatly aAected by thearrangement of triangles in the layout and the magnitude of theangles in individual triangles. The triangles of such a shape, inwhich any error in angular measurement has a minimum eAect

upon the computed lengths, is known as well-conditionedtriangle.


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WELL-CONDITIONED TRIANGLES

The accuracy of a triangulation system is greatly affected by the

arrangement of triangles in the layout, and the magnitude of the

angles in individual triangles. The triangles of such a shape, inwhich any error in angular measurement has a minimum effect upon

the computed lengths, is known as well-conditioned triangle.

5n any triangle of a triangulation system, the length of one side is

generally obtained from computation of the adjacent triangle. Theerror in the other two sides if any, will affect the sides of the

triangles whose computation is based upon their values. 1ue to

accumulated errors, entire triangulation system is thus affected

thereafter.

The best shape of an isoceles triangle is that triangle whose base

angles are :-' each. =owever, from practical considerations, an

e7uilateral triangle may be treated as a well3conditional triangle. 5n

actual practice, the triangles having an angle less than '0: or more

than *0: should not be considered.


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R)*ONNAI!!AN*)

a. B+amination of country to be surveyedb. )uitable site for *ase %inec. $ositions for triangulation stations

d. /etermining

4. Intervisibility. Clearance re3uired in line of sight for

intervisibility

e. Information regarding

4. 0ccess to station. Transport facilities

5. )upply of food, water etc7. Camping ground or suitable accommodation


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!)L)*TION of !TATION!

4. Intervisible. )hould form well conditioned triangles

5. )hould be easily accessible

7. =seful for detail survey

-. Convenientsuitable length of line ofsight


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!TATION %AR2!

4. )hould be permanently marked with copperor bronze tablet on which its name and yearbe stamped

. It should be referenced with atleast tworeference marks and these reference sketchesshould be giving of station and its location

5. )hould be set on concrete monument or

stable rock7. In earth an additional mark be placed about

5( inches below surface in stone or concrete


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TO3)R!

a. In 'at areas or under peculiarconditions towers may be necessary

b. Calculation of height of towerneeded for clearance of line of sight

c. It increases logistic problems


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*O%'UTATION .A4U!T%)NT!

• Dbservations are adusted for

4. Eemoving misclosures

. Consistency


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)trength of Figure

The strength of figure is a factor to be considered in establishing a triangulation system

to maintain the computations within a desired degree of precision. It plays also animportant role in deciding the layout of a triangulation system.

The .!. Coast and "eodetic !ur#eys has de#eloped a con#enient method of

e#aluating the strength of a triangulation figure. It is based on the fact that

computations in triangulation in#ol#e use of angles of triangle and length of one

$nown side. The other two sides are computed by sine law. %or a gi#en change in the

angles, the sine of small angles change more rapidly than those of large angles. Thissuggests that smaller angles less than &'( should not be used in the computation of

triangulation. If, due to una#oidable circumstances, angles less than &'( are used,

then it must be ensured that this is not opposite the side whose length is re)uired to

be computed for carrying forward the triangulation series.

The e*pression gi#en by the .!. Coast and "eodetic !ur#eys for e#aluation of the

strength of figure, is for the s)uare of the probable error (L²)(Si!" pla#e o$ lo%) thatwould occur, if the computations are carried from a $nown side through a single chain

of triangles after the net has been ad+usted for the side and angle conditions. The

e*pression for L is


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)trength of Figure

-

' L> d > R ... (.


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)trength of Figure

5n any triangulation system more than one routes are

possible for various stations. The strength of figure

decided by the factor R alone determines the mostappropriate route to adopt the best shaped

triangulation net route. If the computed value of R

is less, the strength of figure is more and vice

versa.

triangulation (muhammad salman's conflicted copy 2016-04-03)

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