HORIZONTAL POSITION COMPUTATION BY TRAVERSE TRAVERSE COMPUTATIONS AND ADJUSTMENTS

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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At the end of the lecture, the student should be able to: • Define traverse and traverse stations • Enumerate purposes of traverse • Enumerate and differentiate general classes and types of traverse • Identify formulas for traverse adjustments and apply them correctly Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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I. Traverse A. B. C. D.

Definition Purposes General Classes Types

II. Traverse Computations A. Latitude and Departure B. Relative Error of Closure

III. Traverse Adjustments A. Compass Rule B. Transit Rule Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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consists of a series of straight lines connecting successive points whose lengths and directions have been determined from field observations points defining the ends of traverse lines are called traverse stations or traverse points

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

5

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

6

1. Property surveys to locate or establish boundaries. 2. Supplementary horizontal control for topographic mapping surveys. 3. Location and construction layout surveys for highways, railways and other private and public works. 4. Ground control surveys for photogrammetric surveys.

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

7

1. Open Traverse - originates at a point of known position and terminates at a point of unknown position

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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2. Closed Traverse - originates at a point of known position and terminates at a point of known position

Closed Loop Traverse – a closed traverse that originates and terminates at a single point Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Closed Traverse

Closed Loop Traverse

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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1. 2. 3. 4. 5.

Deflection-angle traverse Interior-angle traverse Traverse by angles to the right Azimuth traverse Compass traverse

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

11

In dealing with a closed traverse, we have computations in: 1) Determining latitudes and departures 2) Calculating total error of closure 3) Balancing the survey 4) Determining adjusted positions of traverse stations 5) Area computation 6) Area subdivision Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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 Projection of a line onto a reference meridian or North-South line

 Lines with Northerly bearings (+) LAT  Lines with Southerly bearings (-) LAT

 Equal to distance*cosine of bearing angle

Latitude = d*Cosb Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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 Projection of a line onto a reference parallel or East-West line  Lines with Easterly bearings (+) DEP  Lines with Westerly bearings (-) DEP  Equal to distance*sine of bearing angle

Departure = d*Sineb Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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 Is usually a short line of unknown length and direction connecting the initial and final traverse stations

Note: In computing for q, use the absolute values for SDep and SLat. Determine the quadrant where the line lies using corresponding signs of the 2 sums. Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Ratio of the linear error of closure to the perimeter or total length of the traverse

REC = Relative Error of Closure LEC = Linear Error of Closure D = Total Length or perimeter of the traverse Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Methods of adjustment are usually classified as: I. Rigorous  Least Squares Method

II. Approximate  Compass Rule (or Bowditch Rule)  Transit Rule  Crandall Method Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Named after the distinguished American navigator Nathaniel Bowditch (1773-1838) Based on the assumption that: 1. All lengths are measured with equal care 2. All angles taken with approximately the same precision 3. Errors are accidental 4. Total error in any side is directly proportional to the length of the traverse Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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clat = correction to latitude cdep= correction to departure CL= total closure in lat = SLat

CD= total closure in dep= SDep d = length of any course D = total length of the traverse Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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 No sound theoretical foundation since it is purely empirical  Not commonly used but best suited for surveys where traverse sides are measured by stadia or subtense-bar method  Based on the assumption that:

1. Angular measurements are more precise than linear measurements 2. Errors in traversing are accidental  Not applicable in some instances (lines in E , W, N or S) Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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Where: clat = correction to latitude

cdep= correction to departure CL= total closure in lat = SLat CD= total closure in dep= SDep

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

21

Line

Length(m)

Azimuth (from South)

Line

Length (m)

Azimuth from (South)

AB

495.85

185o30’

DE

1020.87

347o35’

BC

850.62

226o02’

EF

1117.26

83o44’

CD

855.45

292o22’

FA

660.08

124o51’

Compute for: 1. Latitude and Departure of each line 2. Bearing of the side error, LEC, REC 3. Adjust the traverse using Compass Rule 4. Adjust the traverse using Transit Rule Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

22

1. Latitude and Departure of each line Line

Distance (m)

Bearing

Lat (N+, S-)

Dep (E+, W-)

AB

495.85

N 05o30' E

+493.57

+47.53

BC

850.62

N 46o02' E

+590.53

+612.23

CD

855.45

S 67o38' E

-325.53

+791.09

DE

1020.87

S 12o25' E

-996.99

+219.51

EF

1117.26

S 83o44' W

-121.96

-1110.58

FA

660.08

N 55o09' W

+377.19

-541.70

SLat=+16.81

SDep=+18.08

S=5000.13

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

23

2. Bearing of the side error, LEC, REC Bearing of the side error:

 Bearing of the side error is S 47o05’ W Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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2. Bearing of the side error, LEC, REC

LEC = 24.69 m

REC = 1/200 Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

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3. Traverse Adjustment by Compass Rule Line

Distance (m)

Latitude

Departure

Correction (by Compass Rule)

dLat

dDep

Lat_adj

Dep_lat

AB

495.85

493.57

47.53

-1.667

-1.793

491.903

45.737

BC

850.62

590.53

612.23

-2.860

-3.076

587.670

609.154

CD

855.45

-325.53

791.09

-2.876

-3.093

-328.406

787.997

DE

1020.87

-996.99

219.51

-3.432

-3.691

-1000.422

215.819

EF

1117.26

-121.96

-1110.58

-3.756

-4.040

-125.716

-1114.620

FA

660.08

377.19

-541.7

-2.219

-2.387

374.971

-544.087

Sum:

5000.13

16.81

18.08

-16.810

-18.080

0.000

0.000

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

26

3. Traverse Adjustment by Compass Rule Adjusted Values (By Compass Rule) Line

Latitude

Departure

Distance (m)

Bearing

Azimuth (from South)

AB

491.903

45.737

494.025

N 5o19' E

185o19'

BC

587.670

609.154

846.419

N 46o02' E

226o02'

CD

-328.406

787.997

853.692

S 67o23' E

292o37'

DE

-1000.422

215.819

1023.436

S 12o10' E

347o50'

EF

-125.716

-1114.620 1121.687

S 83o34' W

83o34'

FA

374.971

-544.087

N 55o26' W

124o34'

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

660.783

GE 10 – General Surveying I

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4. Traverse Adjustment by Transit Rule Line

Lat

Dep

|Lat|

|Dep|

Correction by Transit Rule

Adjusted Lat/Dep

dLat

dDep

Lat_adj

Dep_adj

AB

493.57

47.53

493.57

47.53

-2.855

-0.259

490.715

47.271

BC

590.53

612.23

590.53

612.23

-3.416

-3.331

587.114

608.899

CD

-325.53

791.09

325.53

791.09

-1.883

-4.305

-327.413

786.785

DE

-996.99

219.51

996.99

219.51

-5.768

-1.194

-1002.758

218.316

EF

-121.96

-1110.58

121.96

1110.58

-0.706

-6.043

-122.666 -1116.623

FA

377.19

-541.7

377.19

541.70

-2.182

-2.948

375.008

-544.648

Sum:

16.81

18.08

2905.77 3322.64 -16.810

-18.080

0.000

0.000

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

28

4. Traverse Adjustment by Transit Rule Adjusted Values (By Transit Rule) Departure Distance Bearing (m)

Line

Latitude

AB

490.715

47.271

492.987

N 5o30' E

185o30'

BC

587.114

608.899

845.849

N 46o03' E

226o03'

CD

-327.413

786.785

852.191

S 67o24' E

292o36'

DE

-1002.758

218.316

1026.248

S 12o17' E

347o43'

EF

-122.666

-1116.623 1123.340

S 83o44' W

83o44'

FA

375.008

-544.648

N 55o27' W

124o33'

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

661.266

Azimuth (from South)

GE 10 – General Surveying I

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SUPPLEMENT TO LAB EXERCISE #2

AZIMUTH ADJUSTMENT

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

30

Azimuth Adjustment • A baseline is usually established first to provide angular check to the traverse • Errors to the observed directions are computed when the baseline is re-observed

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

31

Azimuth Adjustment • AEC (Angular Error of Closure) for an Azimuth Traverse is the deviation between the last observation and the fixed direction of the closing line (baseline) • For Lab Exercise #2,

Note: is an observed quantity is a computed quantity from the given coordinates of the 2 stations Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

32

Azimuth Adjustment Correction to Azimuth:

where: n = number of traverse stations

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

33

Davis, R.E., et. al (1981). Surveying: Theory and Practice. USA: McGraw-Hill, Inc. La Putt, J.P. (2007). Elementary Surveying. Philippines: National Book Store.

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

34

Department of Geodetic Engineering Training Center for Applied Geodesy and Photogrammetry

GE 10 – General Surveying I

35