surveying bec102 5 - traverse

8/13/2019 Surveying BEC102 5 - Traverse

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TRAVERSETRAVERSE

SrSrSITISITI NUR ALIAA ROSLANNUR ALIAA ROSLAN

KLIUCKLIUC


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OverviewOverview

In this lecture we will cover:In this lecture we will cover:

Rectangular and polar coordinatesRectangular and polar coordinates

Definition of a traverseDefinition of a traverse Applications of traversingApplications of traversing

Equipment and field proceduresEquipment and field procedures

Reduction and adjustment of dataReduction and adjustment of data


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Rectangular CoordinatesRectangular Coordinates

EastEast

NorthNorth

Point BPoint B(E(EBB, N, NBB))

N = NNBB -- NNAA

E = EEBB -- EEAAPoint APoint A(E(E

AA

, N, NAA

))

NNBB

NNAA

EEAA EEBB


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Polar CoordinatesPolar Coordinates

EastEast

NorthNorth

d

Point BPoint B

Point APoint A

~ whole-circle bearingd ~ distance


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Coordinate ConversionsCoordinate Conversions

Rectangular to PolarRectangular to Polar

= tan= tan--11 ( E / N )( E / N )

d = ( Ed = ( E22

/ N/ N22 ))

Polar to RectangularPolar to Rectangular

E = d sinE = d sin

N = d cosN = d cos

dNN

EE


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What is a TRAVERSE?What is a TRAVERSE?

A polygon of 2D (or 3D) vectorsA polygon of 2D (or 3D) vectors

Sides are expressed as either polar coordinatesSides are expressed as either polar coordinates

((,d) or as rectangular coordinates differences,d) or as rectangular coordinates differences(E,N)(E,N) A traverse must either close on itselfA traverse must either close on itself

Or be measured between points with knownOr be measured between points with knownrectangular coordinatesrectangular coordinates


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TraverseTraverse

A closed traverseA traverse betweenknown points


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Angles in TraversingAngles in Traversing

Several angles are used in traversing:Several angles are used in traversing:

Interior angles enclosed by the sides of a closedInterior angles enclosed by the sides of a closedtraversetraverse

Exterior angles not enclosed by the sides of a closedExterior angles not enclosed by the sides of a closedtraversetraverse

Deflection: angle between the extension of theDeflection: angle between the extension of the

preceding line and the present onepreceding line and the present one Angle to right the clockwise angle betweenAngle to right the clockwise angle between

preceding line of a traversepreceding line of a traverse


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Applications of TraversingApplications of Traversing

Established coordinates for new pointsEstablished coordinates for new points

(E,N)known

(E,N)known

(E,N)new

(E,N)new


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Applications of TraversingApplications of TraversingThese new points can then be used as aThese new points can then be used as a

framework for mapping existing featuresframework for mapping existing features

(E,N)known

(E,N)known

(E,N)new

(E,N)new

(E,N)new(E,N)new

(E,N)new

(,d)(,d)(,d)

(,d)(,d)(,d)


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Applications of TraversingApplications of Traversing

They can also be used as a basis for setting outThey can also be used as a basis for setting outnew worknew work

(E,N)known

(E,N)known

(E,N)new

(E,N)new


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EquipmentEquipment

Traversing requires:Traversing requires:

An instrument to measure angles (theodolite) orAn instrument to measure angles (theodolite) orbearings (magnetic compass)bearings (magnetic compass)

An instrument to measure distances (EDM or tape)An instrument to measure distances (EDM or tape)


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Measurement SequenceMeasurement SequenceC

D

B

A

E

99.9260.63

129.76

32.20

77.19

232168

352

56

205

21

118

30348

232


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Computation SequenceComputation Sequence

Calculate angular miscloseCalculate angular misclose

Adjust angular miscloseAdjust angular misclose

Calculate adjusted bearingsCalculate adjusted bearings Reduce distance for slope etcReduce distance for slope etc


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Computation Sequence (contd)Computation Sequence (contd)

Compute (E,N) for each traverse lineCompute (E,N) for each traverse line Calculate linear miscloseCalculate linear misclose

Calculate accuracyCalculate accuracy Adjust linear miscloseAdjust linear misclose


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Calculate Internal AnglesCalculate Internal Angles

AdjustmentAdjustment

MiscloseMisclose=(n=(n--2)x1802)x180

303303EE

232232DD

168168CC

1491492052055656BB

97971181182121AA

AdjustedAdjusted

AngleAngle

InternalInternal

AngleAngle

BacksightBacksight

BearingBearing

ForesightForesight

BearingBearing

PointPoint

At each point:

Measure foresight bearing

Measure backsight bearing

Calculate internal angle (back-fore)

For

Bearing to C = 56

Bearing to A = 205

Angle at B = 205 - 56 = 149


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Calculate Angular MiscloseCalculate Angular Misclose

PointPoint ForesightForesight

BearingBearing

BacksightBacksight

BearingBearing

InternalInternal

AngleAngle

AdjustedAdjusted

AngleAngle

AA 2121 118118 9797

BB 5656 205205 149149

CC 168168 232232 6464

DD 232232 352352 120120

EE 303303 4848 105105

=(n=(n--2)x1802)x180 535535MiscloseMisclose --55

AdjustmentAdjustment --11


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Calculate Adjusted AnglesCalculate Adjusted Angles

PointPoint ForesightForesight

BearingBearing

BacksightBacksight

BearingBearing

InternalInternal

AngleAngle

AdjustedAdjusted

AngleAngle

AA 2121 118118 9797 9898

BB 5656 205205 149149 150150

CC 168168 232232 6464 6565

DD 232232 352352 120120 121121

EE 303303 4848 105105 106106

=(n=(n--2)x1802)x180 535535 540540MiscloseMisclose --55

AdjustmentAdjustment --11


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Compute Adjusted BearingCompute Adjusted Bearing

Adopt a starting bearingAdopt a starting bearing Then, working clockwise around the traverse:Then, working clockwise around the traverse:

Calculate reverse bearing to backsight (forward bearingCalculate reverse bearing to backsight (forward bearing180180))

Subtract (clockwise) internal adjusted angleSubtract (clockwise) internal adjusted angle Gives bearing of foresightGives bearing of foresight

For example (bearing of line BC)For example (bearing of line BC)

Adopt bearing of ABAdopt bearing of AB 2323 Reverse bearing BA (=23Reverse bearing BA (=23+180+180)) 203203 Internal adjusted angle at BInternal adjusted angle at B 150150 Forward bearing BC (=203Forward bearing BC (=203--150150)) 5353


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Compute Adjusted BearingsCompute Adjusted Bearings

LineLine ForwardForwardBearingBearing

ReverseReverseBearingBearing

AdjustedAdjustedAngleAngle

ABAB 2323 203203 150150

BCBC 5353

CDCD

DEDE

EAEA

ABAB

C

D

E

A

B

53

203

150


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ABAB 2323 203203 150150

BCBC 5353 233233 6565

CDCD 168168

DEDE

EAEA

ABAB

C

D

E

A

B

233

23

65168


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ABAB 2323 203203 150150

BCBC 5353 233233 6565

CDCD 168168 348348 121121

DEDE 227227 4747 106106

EAEA --5959

301301

ABAB

C

D

E

A

B

53

23

106

168

47

301


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ABAB 2323 203203 150150

BCBC 5353 233233 6565

CDCD 168168 348348 121121

DEDE 227227 4747 106106

EAEA 301301 121121 9898

ABAB 2323 (check)(check)

C

D

E

A

B

53

23

98

168

227

121


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(E,N) for each line(E,N) for each line

The rectangular components for each line areThe rectangular components for each line arecomputed from the polar coordinates (computed from the polar coordinates (,d),d)

E = d sinE = d sin N = d cosN = d cos

Note that these formulae apply regardless of theNote that these formulae apply regardless of thequadrant so long as whole circle bearings arequadrant so long as whole circle bearings areusedused


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Linear Misclose & AccuracyLinear Misclose & Accuracy

Convert the rectangular misclose components toConvert the rectangular misclose components topolar coordinatespolar coordinates

Accuracy is given byAccuracy is given by1: (traverse length / linear misclose)1: (traverse length / linear misclose)

= tan= tan--11

( E / N )( E / N )d = ( Ed = ( E22 / N/ N22 ))


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Quadrants and tan functionQuadrants and tan functionN

E+

+

-

-

--

++

positiveokay

negativeadd 360

positiveadd 180

negativeadd 180


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For the exampleFor the example

Misclose (E,N)Misclose (E,N) (0.07,(0.07,--0.05)0.05)

Convert to polar (Convert to polar (,d),d) == --54.4654.46(2(2ndnd quadrant) = 125.53quadrant) = 125.53 d = 0.09 md = 0.09 m

AccuracyAccuracy 1 : ( 399.70 / 0.09 ) = 1 : 44411 : ( 399.70 / 0.09 ) = 1 : 4441


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Bowditch AdjustmentBowditch Adjustment

The adjustment to the easting component of anyThe adjustment to the easting component of anytraverse side is given by:traverse side is given by:

EEadjadj = E= Emiscmisc x side length/ total perimeterx side length/ total perimeter

The adjustment to the northing component ofThe adjustment to the northing component ofany traverse side is given by:any traverse side is given by:

NNadjadj = N= Nmiscmisc x side length/ total perimeterx side length/ total perimeter


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The ExampleThe Example

East miscloseEast misclose 0.07m0.07m

North miscloseNorth misclose --0.05m0.05m

Side ABSide AB 77.19m77.19m

Side BCSide BC 99.92m99.92m

Side CDSide CD 60.63m60.63m

Side DESide DE 129.76m129.76m

Side EASide EA 32.20m32.20m

Total perimeterTotal perimeter 399.70m399.70m


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Exercise 1Exercise 1

Vector ComponentsVector Components(pre(pre--adjustment)adjustment)SideSide EE NN EEadjadj NNadjadj EEcorrcorr NNcorrcorr

ABAB 30.1630.16 71.0571.05

BCBC 79.879.8 60.1360.13

CDCD 12.6112.61 --59.3159.31

DEDE --94.9094.90 --88.5088.50

EAEA --27.6027.60 16.5816.58

MiscMisc (0.07)(0.07) ((--0.05)0.05)


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The Adjustment ComponentsThe Adjustment Components

SideSide EE NN EEadjadj NNadjadj EEcorrcorr NNcorrcorr

ABAB 30.1630.16 71.0571.05 0.0140.014 --0.0100.010

BCBC 79.879.8 60.1360.13 0.0160.016 --0.0120.012

CDCD 12.6112.61 --59.3159.31 0.0110.011 --0.0080.008

DEDE --94.9094.90 --88.5088.50 0.0230.023 --0.0160.016

EAEA --27.6027.60 16.5816.58 0.0060.006 --0.0040.004

MiscMisc (0.07)(0.07) ((--0.05)0.05) (0.070)(0.070) ((--0.050)0.050)


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Adjustment Vector ComponentsAdjustment Vector Components

SideSide EE NN EEadjadj NNadjadj EEcorrcorr NNcorrcorr

ABAB 30.1630.16 71.0571.05 0.0140.014 --0.0100.010 30.14630.146 71.06071.060

BCBC 79.879.8 60.1360.13 0.0160.016 --0.0120.012 79.78479.784 60.14260.142

CDCD 12.6112.61 --59.3159.31 0.0110.011 --0.0080.008 12.59912.599 --59.30259.302

DEDE --94.9094.90 --88.5088.50 0.0230.023 --0.0160.016 --94.92394.923 --88.48488.484

EAEA --27.6027.60 16.5816.58 0.0060.006 --0.0040.004 --27.60627.606 16.58416.584

MiscMisc (0.07)(0.07) ((--0.05)0.05) (0.070)(0.070) ((--0.050)0.050) (0.000)(0.000) (0.000)(0.000)


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Exercise 2Exercise 2

Calculate the adjusted coordinates for stations B,Calculate the adjusted coordinates for stations B,C, D, E and FC, D, E and F

Adjust any misclosures by using the BowditchAdjust any misclosures by using the Bowditchmethodmethod

The coordinates for station A is 500 E andThe coordinates for station A is 500 E and1000N1000N

Whole Circle Bearing for line AF is 70Whole Circle Bearing for line AF is 7000000000


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13313354405440

11011030003000

13013036203620

11511511201120

959500200020

12912949204920

372.47526.72

287.40

301.83

656.54

429.37

707000000000

NF

A

B

C

D

E

surveying bec102 5 - traverse

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