TRAVERSE COMPUTATIONS AND ADJUSTMENTS PDF

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TRAVERSE COMPUTATIONS AND ADJUSTMENTS Engr. Jeark A. Principe, MSc. Department of Geodetic Engineering (DGE) Training Center for Applied Geodesy and Photogrammetry (TCAGP) At the end of the lecture, the student should be able to:  Define traverse and traverse stations  Enumerate purposes of traver...

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TRAVERSE COMPUTATIONS AND ADJUSTMENTS

Engr. Jeark A. Principe, MSc. Department of Geodetic Engineering (DGE) Training Center for Applied Geodesy and Photogrammetry (TCAGP)

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 

I.

Traverse A. Definition

B. Purposes C. General Classes D. Types II.

Traverse Computations A. Latitude and Departure B.

III.

Relative Error of Closure

Traverse Adjustments A. Compass Rule B.

Transit Rule



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

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.

1.

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

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

Closed Traverse

Closed Loop Traverse

1. 2. 3. 4. 5.

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

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

 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

 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

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

LEC  (Dep)  (Lat ) 2

2

  Dep  Tan      Lat  Note: In computing for , use the absolute values for Dep and Lat. Determine the quadrant where the line falls using corresponding signs of the 2 sums.

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

LEC REC  D REC = Relative Error of Closure LEC = Linear Error of Closure D = Total Length or perimeter of the traverse

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

II. Approximate  Compass Rule (or Bowditch Rule)  Transit Rule  Crandall Method

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 are 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

clat c dep

d  C L   D d  C D   D

clat = correction to latitude cdep= correction to departure CL= total closure in lat = Lat CD= total closure in dep= Dep d = length of any course D = total length of the traverse

 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 subtensed 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)

clat

| Lat | (C L )   Lat

Where: clat = correction to latitude cdep= correction to departure

c dep

| Dep | (C D )   Dep

CL= total closure in lat = Lat CD= total closure in dep= Dep

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’

Note: Coordinates of A are Compute for: NA=20,000.000, EA=20,000.000 1. Latitude and Departure of each line 2. Bearing of the side error, LEC, REC 3. Adjust the traverse and compute for the adjusted coordinates of traverse stations using Compass Rule 4. Adjust the traverse and compute for the adjusted coordinates of traverse stations using using Transit Rule 5. Provide a sketch of the traverse

1. Latitude and Departure of each line Line

Distance (m)

AB

495.85

BC

850.62

CD

855.45

DE

1020.87

EF

1117.26

FA

660.08

=5000.13

Bearing

Lat (N+, S-)

Lat=

Dep (E+, W-)

Dep=

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

Lat=+16.81

Dep=+18.08

=5000.13

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



tan b  18.08

 16.81

 1.075550268

b  47 0 05'  Bearing of the side error is S 47o05’ W

2. Bearing of the side error, LEC, REC Linear Error of Closure (LEC):

 (16.81) 2  (18.08) 2  24.687

LEC = 24.69 m

Relative Error of Closure (REC):

24.69  5000.13 1 1  say 202.52 200

REC = 1/200

3. Traverse Adjustment by Compass Rule

Line

Correction Distance Latitude Departure (by Compass Rule) (m) dLat dDep

AB

495.85

BC

850.62

CD

855.45

DE

1020.87

EF

1117.26

FA

660.08

Sum:

5000.13

Lat_adj

Dep_lat

3. Traverse Adjustment by Compass Rule

Line

Correction Distance Latitude Departure (by Compass Rule) (m) 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

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

Latitude Departure

AB

491.903

45.737

BC

587.670

609.154

CD

-328.406

787.997

DE

-1000.422

215.819

EF

-125.716 -1114.620

FA

374.971

-544.087

Distance (m)

Bearing

Azimuth (from South)

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

N 55o26' W

124o34'

-544.087

660.783

3. Traverse Adjustment by Compass Rule

A

B C D E F A

Adjusted Values (By Compass Rule) Latitude Departure Northing Easting 20000.000 20000.000 491.903 45.737 20491.903 20045.737 587.67 609.154 21079.573 20654.891 -328.406 787.997 20751.167 21442.888 -1000.422 215.819 19750.745 21658.707 -125.716 -1114.62 19625.029 20544.087 374.971 -544.087 20000.000 20000.000

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

-2.948

375.008

-544.648

Sum:

16.81

18.08

2905.77 3322.64 -16.810 -18.080

0.000

0.000

541.70

-2.182

4. Traverse Adjustment by Transit Rule

Line

Adjusted Values (By Transit Rule) Latitude Departure Distance Bearing Azimuth (m) (from South)

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

N 55o27' W

124o33'

-544.648

661.266

4. Traverse Adjustment by Transit Rule

A

B C D E F A

Adjusted Values (By Transit Rule) Latitude Departure Northing Easting 20000.000 20000.000 490.715 47.271 20490.715 20047.271 587.114 608.899 21077.829 20656.170 -327.413 786.785 20750.416 21442.955 -1002.758 218.316 19747.658 21661.271 -122.666 -1116.623 19624.992 20544.648 375.008 -544.648 20000.000 20000.000

5. Sketch of the traverse C

N

D

100 m

B

A E F

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....