Computation And Balancing of Traverse Area in King ...

Journal of Computing Technologies (2278 – 3814) / #56 / Volume 4 Issue 1

Computation And Balancing of Traverse Area in King Khalid University Saiful Islam#1, Sham Al Deen M.Saad *2, Sohaib nazar*3 Roohul Abad Khan#4 #1* 3# 4

Lecturers, Department of Civil Engineering, King Khalid University, Abha 61441 Saudi Arabia 1 [email protected] *2 Assistant Professor, Department of Civil Engineering, King Khalid University, Abha 61441 Saudi Arabia 2 [email protected] Abstract— The Advent of modern Surveying Instrument such as Total Station and advancement in computing industry has made it desirable to do the traversing work accurately. The paper deals with Traversing five points namely A, B, C, D and E using Total Station. Parameters such as horizontal distance, horizontal angles of all points were measured. It is essential to check the error of closure for interior angles. Moreover the Fore bearing of Survey line AB is taken out and with the help of this bearing and included angle the bearing of all other line can be computed. The observations are then used for different traverse balancing techniques. The balanced unknowns and observations were computed precisely to about a few millimeters and seconds of accuracy. Moreover new Bearings and Length are computed from the result of each of the balancing techniques and compared. Keywords— Total station, Traversing, Balancing, Bowditch Method, Transit Method, Least Square Method

I. INTRODUCTION The most frequently used surveying instrument today is the total station. Total station systems contain three components: the distance measuring unit or EDM, the angle measuring device or theodolite, and an onboard microprocessor [8]. Total stations have considerably increased the amount of topographic data that can be collected during a day. Modern total stations are also planned for construction stakeout and highway centreline surveys [7]. Horizontal and vertical traversing are the new important applications using total station. The linear misclosures of the traverse must be adjusted. Shepherd [11], lists some of the traverse adjustments that may be used: Bowditch, Transit, Crandall, method. The common virtue of these adjustment methods is their mathematical simplicity. Unfortunately these techniques are non-rigorous and often based on assumptions. The method of least squares is a rigorous technique that can be applied to the adjustment of single traverses as well as networks of connected traverses to yield the most likely values of the survey measurements. Leahy [10] has an excellent summary of the theoretical basis and development of the least squares technique. The most commonly used method is the compass rule. It is based on the assumption that the quality of distance and angular measurements is more or less the same. It is particularly applicable to surveys made with total stations [2]. Total station instruments can quickly transfer threedimensional coordinates and are capable of storing unique mapping feature codes and other parameters. One of the finest features of the total station is the ability to download data directly into a computer without human errors

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[7]. Total station gives range, azimuth and elevation from its position to that of a landmark or a reflecting prism [9] . The development of the no prism total station has made it possible for only one person to carry out field measurements [3]. Modern total stations have an inbuilt data collector. The first step of traversing process is the field survey. Most total stations provide the facility to download data to a personal computer via a cable or Bluetooth connection rather than using a data card [4]. II. TRAVERSE MEASUREMENT Traverses are a series of established stations that are tied together by angle and distance [1]. There are two types of traverses, closed traverses and open traverses. Two categories of closed traverses exist, polygon and link. In the polygon traverse the lines return to the starting point. Link traverses finish upon another station that should have a positional accuracy equal to or greater than that of the starting point. The link type must have a closing reference direction [5]. An open traverse neither forms a closed geometric figure nor does it end at a point of known position [6] The field data are downloaded to a computer. The download computer program is normally supplied by the total station manufacturer, and the actual transfer can be sent through a USB cable. Once the data are in the computer, the data must be translated into a format that is compatible with the computer program that will process the data [1]. Errors made in the field can be adjusted at this stage. . A. Bowditch Method CL=L xl/l

(1)

CD=D xl/l

(2)

Where CL=correction to latitude of any line CD =correction to departure of any line L =total error in latitude D =total error in departure l =total length of traverse or perimeter p l =length of that line for which the correction is being computed.

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B. Transit Method CL=L xL/LT

(3)

CD=D xD/DT

(4)

IV. INPUT DATA Total station is chosen to collect data for traversing five point in field. The readings of length of all sides and bearings are shown in table 1 TABLE I

CL=correction to latitude of any line CD =correction to departure of any line

LENGTH AND BEARING OF TRAVERSE

Line

Length

L =latitude of any line D =departure of any line LT=arithmetic sum of latitudes (ignoring the signs) DT =arithmetic sum of departures (ignoring the signs) L =

total error (algebraic sum) in latitude,

D =

total error (algebraic sum) in departure

m

D

M

S

AB

22.44

100

42

37

BC

19.66

38

18

30

CD

38.5

313

36

51

DE

31

260

57

24

EA

40.61

142

53

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V. BALANCING OF TRAVERSE

C. Least Square Method. The least squares method provides a general and systematic procedure which yields a unique solution in all situations. Assuming that all the observations are uncorrelated then the least squares method of adjustment is based upon the following criterion: “The sum of the weighted squares of the residuals must be a minimum”. III. STUDY AREA The traverse work is done inside the King Khalid University Campus beside Work area, Abha, Kingdom of Saudi Arabia. Abha is the capital of Asir province in Arabia. It is located in the Southern Region of Asir. It is situated at (2,200 meters) above sea level .The climate of Abha is cold semi-arid climate. The city is generally mild throughout the year, though it’s noticeably cooler during the “low-sun” season. Abha seldom sees temperatures rise above 35 degree Celsius during the course of the year. The city averages 600 mm of rainfall annually, with the bulk of the precipitation occurring between February and April, with a secondary minor wet season of July and August. The map shown below in figure depicts the location of Study Area. . .

Bearing

The field data available from total station traversing is employed for computation of traverse work. The error involve in performing the survey work are then balanced by three method which are tabulated as follows TABLE III BALANCING BY BOWDITCH METHOD Corrected Latitudes

Corrected Departures

-4.252

22.013

15.356

12.156

26.418

-27.936

-4.985

-30.664

-32.537

24.431

TABLE IIIII BALANCING BY TRANSIT METHOD

Corrected Latitudes -4.198

Corrected Departures 22.003

15.325

12.162

26.382

-27.932

-4.905

-30.679

-32.604

24.446

TABLE IVV BALANCING BY LEAST SQUARE METHOD

Corrected Latitudes -4.228

Corrected Departures 21.941

15.245

12.125

26.407

-27.944

-4.972

-30.710

-32.452

24.588

Fig. 1 Study Area


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This is well known fact that least square method is rigorous method and superior to all method of balancing. So in the present research work, the corrected Length and Bearing of network obtained from least square method is taken as standard result and error in length and bearing can be computed for other two methods. The results are shown in figure 6-9

1000 800 600 400 200 0

Bowditch Transit Least Square Method

0 1 2 3 4 5 6 Side

Fig. 4

% Error in Bearing

From table 2, 3, 4 we can get correct Length of all the line using correct latitudes and departures for all the three methods. Using the corrected length and observed length we can get error and error% in length. The results for error in length and % error in length measurement are shown in fig 2 and 3. Similarly the corrected bearings can be computed out. The results for error in bearings and % error in bearings measurement is shown in fig 4 and 5.

ΔBearing in (seconds)

VI. RESULTS

0.6 0.4

Bowditch

0.2

Transit Least Square

0 0

2

4

6

Side

ΔL in (m)

Fig .5

1

0.15 0.1 0.05 0

AB

BC

CD

DE

EA

Bowditch 0.07

0.1

0

0.04

0.03

Transit

0.08

0.03

0.04

0.04

0.04

Side

Bowditch

0.5

Transit 0 0

5

10

Fig. 6 ΔL in (m) taking Corrected Least square reading as base

Least Square

Side

Fig. 3

% Error in Length

% Error in Length

Fig. 2

0.60 0.40 0.20 0.00

AB

BC

CD

DE

EA

Bowditch 0.31

0.51

0.00

0.13

0.07

Transit

0.41

0.08

0.13

0.10

0.18

Side Fig .7 % Error in Length taking Corrected Least square reading as base


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ΔBearing in Degree


0.3 0.2 0.1 0

BC

CD

DE

EA

Bowditchrule 0.03

AB

0.16

0.02

0.04

0.25

Transit rule

0.08

0.01

0.11

0.28

0.09

ACKNOWLEDGMENTS We would like to express our sincere thanks to Prof. Dr.Hussein Manie Ahmed AL Wadai Dean College of Engineering, King Khalid University, Abha City and Dr. Ibrahim Falqi, Vice Dean for providing us encouraging environment for the research. REFERENCES

Side

% Error in Bearing

Fig. 8 ΔBearing in (degree) taking Corrected Least square reading as base

0.6 0.4 0.2 0

[2] McCormac , Jack , Sarasua , Wayne and Davis , William , " Surveying " , Sixth Edition , John Wiley & Sons , United States of America , 2013 .

AB

BC

CD

DE

EA

Bowditchrule 0.03

0.41

0.01

0.01

0.17

Transit rule

0.21

0.01

0.04

0.19

0.08

Side Fig. 9 % Error in bearing taking Corrected Least square reading as base

VII. CONCLUSIONS After evaluating the results of the foregoing findings, the following conclusions were drawn: 1. The observations angles should be equal to the allowable sum of interior angle in traverse survey 2.

3.

4.

5.

[1] Kavanagh , Barry F. and Mastin , Tom B. , " Surveying : Principles and Applications " , Ninth Edition , Pearson , United States of America , 2014 .

The latitude and departure of network points can be determined as long as the angles and distances of the network have been determined. So, this network should be Balanced through transit, compass rule and Least Square Having the Balancing of both latitude and departure been determined, the Corrected length and bearing can be find out. Least Squares is an Balancing technique founded on well accepted principles of measurements and their errors and is regarded as superior to all other methods of Balancing. So its result can be treated as standard one and the result from Bowditch and Transit method can be compared with this

[3] Yan , F. , Ullah , M.R. , Gong , Y. , Feng , Z. , Chowdury , Y. and Wu , L. , "Use of a No Prism Total Station for Field Measurements in Pinus Tabulaeformis Carr. Stands in China " , Biosystems Engineering , Volume 113 , Pages 259-265 ,2012 . [4] Bedford , Jon , Pearson , Trevor , Thomason , Bernard and Al Oswald ," Traversing the Past : The Total Station Theodolite in Archaeological Landscape Survey " , English Heritage , 2011 . [5] Ghilani , Charles D. and Wolf , Paul R. , " Elementary Surveying : An Introduction to Geomatics " , Thirteenth Edition , Pearson Education Limited , Edinburgh Gate , Harlow , United States of America , 2011 . [6] Nathanson , Jerry , Lanzafama , Michael T. and Kissam , Philip , "Surveying Fundamentals and Practices " , Sixth Edition , Pearson Education International , United States of America , 2011 . [7] Gopi , Satheesh , Sathikumar , R. and Madhu , N. , " Advanced Surveying : Total Station , GIS and Remote Sensing " , First Impression , Dorling Kindersley , India ,2007 [8] Anderson , James M. and Mikhail , Edward M. , " Surveying : Theory and Practice " , Seventh Edition , McGraw Hill Companies , United States of America ,1998. [9] Lloret , P. , " Inertial + Total Station + GPS for High Productivity Surveying " ,Position Location and Navigation Symposium , IEEE Plans , Pages 338-346 , 1990. [10] Leahy, F.J., 1974. 'Two hundred years of adjustment of survey measurements', Two Centuries of Surveying (1874-1974-2074): Proceedings of The Institution of Surveyors, Australia, 17th Australian Survey Congress, Melbourne, 23 February -1 March 1974, pp.19-29. [11] Shepherd, F.A., 1968. Surveying Problems and Solutions, Edward Arnold Ltd., London.

The accuracy obtained by total station traverse reveals the fact that it is suitable for most engineering works. Pages 338-346 , 1990. [10] Leahy, F.J., 1974. 'Two hundred years of adjustment of survey measureme


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BIOGRAPHY Mr. Saiful Islam is presently Lecturer in the Civil Engineering Department, King Khalid University, Abha ,Kingdom of Saudi Arabia . He has over 5 years of teaching, research, experiance. He did his B.Tech degree from Zakir Hussain College of Engineering, A.M.U, Aligarh. He has completed his M.Tech degree from Indian Institute of Technology, Roorkee. He is the life member of Indian Society of Technical Education, International Association of Engineers and International Association of Protective Structures. He is the author of Engineering Geology, Building materials and Construction, Hydraulics and Hydraulic Machines, Geological Sciences, Open channel flow and Geoinformatics as well. He has published several papers in International journal. He has attended several conferences/ Workshops.


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