Economical Applications of GPS in Road Projects in India

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1 Aville online t ScienceDirect Procedi - Socil nd Behviorl Sciences 96 ( 013 ) th COTA Interntionl Conference of Trnsporttion Professionls (CICTP 013) Economicl Applictions of GPS in od Projects in Indi S.M.Prsnn Kumr, S.K. Mhjn * Director, CET, ungt Eductionl Cmpus, Kohk Kurud od, Bhili Chhttisgrh Indi Professor, Civil Engineering Deprtment, CET, ungt Eductionl Cmpus, Kohk Kurud od, Bhili Chhttisgrh Indi Astrct The Glol Positioning System (GPS) is stellite sed nvigtion system mde up of network of 4 stellites plced into orit y U.S. Deprtment of Defense. GPS ws originlly intended for militry pplictions, ut in the 1980s, they mde the system ville for civilin use. GPS works in ny wether conditions, nywhere in the world, 4 hours dy. Therefore it fcilittes everydy ctivities such s nking, moile phone opertions nd even the control power grids y llowing well synchronized hnd-off switching. In generl GPS pplictions re relized in following: In Air nvigtion y generl vition nd commercil ircrft At Se nvigtion y recretionl oters, commercil fishermen, nd professionl mriners For Surveyors cost sving y drsticlly reducing setup time t the survey nd providing incredile ccurcy All ove pplictions employ the service of 4- stellites in the orit t ny point of time. In this pper new method is suggested for which, softwre is eing developed to get the GPS outputs mking use of dt from single stellite. The - stellites, therefore it would cut down the finncil impliction to lrge extent in ny project. GPS ppliction in od projects is discussed herein with this new concept. 013 The Authors. Pulished y Elsevier y Elsevier Ltd. Open B.V. ccess under CC BY-NC-ND license. Selection nd/or peer-review peer-review under under responsiility responsiility of Chinese of Chinese Overses Overses Trnsporttion Trnsporttion Assocition Assocition (COTA). (COTA). Trversing; Gloemtic Science; Geomtic Engineering; od Surveys; Geometricl figures; Glol Positioning System (G.P.S.) 1. GPS Appliction in Current Prctice There re 4 stellites tht mke up GPS spce segment Fig.1. All the stellites re oriting the erth out 0,000 km ove us. They re constntly moving, mking complete orits in less thn 4 hours. These stellites * Corresponding uthor. Tel.: ; fx: E-mil ddress: ngelvlleyhili@gmil.com The Authors. Pulished y Elsevier Ltd. Open ccess under CC BY-NC-ND license. Selection nd peer-review under responsiility of Chinese Overses Trnsporttion Assocition (COTA). doi: /j.sspro

2 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) re trvelling t speed of 11,500 km per hour. They re powered y solr energy. They hve ckup tteries on ord to keep them running in the event of solr eclipse. Smll rocket oosters on ech stellite keep them loction. Essentilly GPS receiver compres the time of trnsmitting signl to the stellite with the time it receives signl from it. The time difference tells the GPS receiver position. The mthemticl principle clled triltertion requires distnce mesurements from few more stel this informtion to deduce its own loction. Finlly the loction of GPS receiver is clculted in terms of ltitude, longitude nd elevtion. Fig.1. GPS the spce segment of US stellites In order to mke simple clcultions the GPS receiver hs to know following dt: The loction of t lest three stellites in the spce The distnce etween trnsmitting point nd ech of the 3 stellites The GPS receiver provides two informtion y nlyzing high frequency, low power rdio signls from GPS stellites (see Fig..) Fig.. GPS Principle of working

3 80 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) In simple mthemticl terms: GPS receivers: Mesure t r Decode t c Compute G.P.S. is employed to monitor ground ojects with respect rtificil stellites lunched in spce. 0ften we need to trck the route of moving vehicle to determine fuel consumption, locte its position nd the speed etc. Such dt is essentil for efficient mngement of n orgniztion. Fig.() Shows the concept of working of G.P.S. device. To locte the position nd trce the pth of moving vehicle for efficient mngement of ny concern such system is mounted on vehicle which receives signls from three stellites s per conventionl method of working. Mthemtics involved in determining the ground position is pprent from following Fig.(3) Principle of GPS positioning: Stellite 1 sends signl t time t e1 Ground receiver receives its signl t time t r The rnge mesurement p 1 to stellite 1 is : op 1 = (t r -t e1 ) x speed of light owe re therefore locted on sphere with rdius p1 centered on stellite 1 3 stellites intersection of 3 spheres Fig.3. GPS Locting the position of receiver on erth Nomenclture loction of 3 stellites in spce (X s,y s,z s ) (X r,y r,z r ) simultneous rnge mesurement from receiving sttion c velocity of light = m/s smllest side of the tringle side greter thn in the tringle the rdius of the circum-circle of given tringle ABC

4 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) New Geometricl Concept Glol Mth Concept invented very recently y Dr. S.K. Mhjn, Indi [15] in 008 hs revolutionized field surveying opertion ecuse less dt is oserved in the field to mke geometricl figures. Conventionlly we require minimum three elements out of six (3sides+3ngles) to mke tringle. Glol Mth mkes use of only two elements to mke tringle insted of three therefore it finds wide ppliction in civil engineering, prticulrly rod survey works vi: tringultion, trversing nd triltertion. Glol Mth Appliction Softwre [5], is known s Geomtic Engineering Softwre. It hs rought chnges in od Surveying Equipment nd Process to nlyze dt for end results. A closed trverse survey consists of series of tringles, whose lengths nd directions re mesured etween connecting points on proposed rod lignment. The principle of Geomtic cse they cn e represented given y: (1) Aove formul is derived y using geometric properties of tringle relted with circle (Annexure I). It is pprent tht only two sides (, nd ) re sufficient to determine the rdius. Thus tringle cn e mde with the use of only two elements simply joining Fig.4. Explicit Orienttion of two element tringle orienttion Explicit orienttion of two element tringles cn e chieved in following steps. It is pprent from sic opertions in surveying tht tringle is n integrl unit in the process of oserving dt of trverse. It is found tht with ingenious choice of elements nd oservtion plnning, requirement of elements to mke tringle cn e curtiled to two. The two element tringle construction nd its explicit orienttion cn e done in following steps: Step 1- In the tringle Fig.4, sides s,, c re 3 sides out of which two sides nd re (1) Step - There cn e three possile orienttion of tringle formed with sides n 1. ( & ). The correct one cn e resolved with respect to previling physicl condition. determined from eq.(1) needs to e corrected for its explicit orienttion [1]. It is chieved s follows: i. - Correction to for rt. Property Fig.1. ( y eq.(1) is to e corrected if tringle ABC is rt. tringle. According to Pythgors theorem we hve:

5 804 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) The correction to cn e explined through Pythgors triplet e.g. 3, 4, 5 s sides, nd c. Let = 3, nd = 4, sustituted in eq.(1). We get =.64 Applying Pythgors check 3 +4 = 5, or side c = 5 =, ut from eqution (1) we get = hence correction to () is ii. Explicit Orienttion of d ngle etween nd is cute Fig.(1-) After computing from eq.(1) perform following steps: = +c c Cos(x) () Eq.() is qudrtic in c, therefore two vlue C) is computed iii. Explicit Orienttion of when included ngle etween nd is otuse Included ngle etween given sides nd computed in step, will give exterior ngle (180 C) nd the cn e produced with given sides nd nd included ngle s otuse ngle. 3. GPS Triltertion in od Works Fig.5. Triltertion in rod surveys Bsic oute Survey nd Design works re crried out y GPS in following steps: 1. Concept for oute. econnissnce Study - -. Identify Alterntive outes (corridors). Corridor Study 3. Alignment Design 4. odwy Design 5. Design rodwy items 6. ight of wy surveys 7. Construction surveys 8. Plnning GPS Surveys s importnt s the sophisticted needed to collect the dt

6 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) Modified Working of G.P.S. with Single Stellite The new geometric concept descried ove could e employed to modify GPS working y receiving dt from only one spce stellite to furnish the end results. It is explined y n exmple of use of G.P.S. trcking of n Engineering College Bus with use of single stellite oservtions refer Fig. (6): Solution: Fig.6. G.P.S. dt otined from trcking single stellite 1. Let Delhi () e the control sttion to supply/eceive informtion to GPS SV (Geocentric stellite pressed s (Xi, Yi, Zi). S is position of geocentric stellite t the time of trcking of College Bus 3. A,B,C,D,E sttions on us route emitting e-m wve signls from College Bus crrying trnsmitter during the time of its trvel. Let the us route is defined y green trck ABCDEA. 4. E-M wve time signls re trnsmitted to stellite S is hving tomic clock. Therefore distnces: SA, SB, SC, SD, SE nd S re computle y multiplying time nd e-m wve length. The distnces re mrked in lck colour with rrows. 5. From verticl tringles SA, SB, SC, SD nd SE oserved in (4), distnces A, B, C, D nd E re computed using two elements tringle theory given y uthors. These distnces re mrked in red colour in the Fig. (6) 6. Pir of distnces known in step (5), re used to get distnces AB, BC, CD, DE, nd EA gin y two elements tringle theory, to plot the trverse (Bus oute) ABCDEA. To illustrte the ppliction, Let us consider the verticl tringle SA in which two sides S nd SA re otine The computed lengths: S = 3165 km = () nd AS = 3800 km = () re sustituted in eq.(1) to determine A = km. The oservtion nd computtion sheet is completed elow for ll verticl tringles formed during the movement of the us from sttion A to E.

7 806 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) Tle 1. No Computed Distnces Computed side from two () Using E.M. Wves () 1 SA S = 3165 km SA = 3800 km A = km SB S = 3165 km SB = 3805 km B = km 3 SC S = 3165 km SC = 381 km C = km 4 SD S = 3165 km SA = 3807 km D = km 5 SE S = 3165 km SE = 3798 km E = km The computtion sheet elow shows the solution of horizontl tringles Fig.6 formed on the erth surfce: Tle. No Computed Distnces tle-1 Computed side from pir () Using Two (1) 1 AB A = km B = km AB = km BC B = km C = km BC= 6.05 km 3 CD D = km C = km CD= km 4 DE E = km D = km DE = km 5 EA E = km A = km AE = 8.13 km It is pprent from ove tles tht the us route (trverse ABCDEA perimeter = km) is completely determined nd cn e plotted. A seprte locl survey level net my e run from sttion A to points B, C, D nd E if height coordintes of the points re lso required. Glol Coordintes (x i, y i, z i ) of the trverse points cn e determined s explined elow: Let the coordintes of e (0,0,0), the zimuth of sight A t the time of oservtion =00 As zimuth is 00, the x coordinte of S = 3165 sin (0) = km, nd y coordinte of S = 3165 Cos (0) = km. Similrly the coordintes (x i, y i, z i ) of trverse points A, B, C, D nd E cn e worked out. 5. Use of GPS to Identify Trffic Prolems GPS surveys hve een conducted to initite widening of rods from two to four lnes with pved shoulders, on certin existing stretches/ corridors of Ntionl Highwys in the country. It hs direct impct on mny urn stte rods joining min highwys. One of the prolems rose due to extension work etween ipur nd Durg cities on Ntionl Highwy No. 6. is highlighted elow in Fig.(7) mrked with lue line. As result of widening of NH-6 the trffic jm on stte rod 330 m long etween rotries (1) nd () hs incresed.

8 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) Geomtic engineering softwre in rod surveys- Fig.7. Ntionl Highwy 6 (Indi) Trffic prolem stted ove cn e solved y providing fly over etween the two otries. Therefore loction survey to find out suitle route lignment of fly over is crried out. The tchometric trverse dt oserved t the site is shown with red lines in the key Pln Fig. 8. Min fetures of Trverse survey shown in the Fig.8 re: 1. 1 nd re two existing rotries distnce etween them is 330 m.. od from 1 to Durg city direction rnches into two viz: NH- on Other prominent fetures like Dhillon Hotel, Chndull Chndrkr Memoril Hospitl, Existing otry 3, etc. re mrked for identifiction Fig.8 Key Pln to conduct Tchometric Trverse Further there is level crossing gte in etween 1 nd Fig. 8., whose frequent movement due to ll kinds of trins, Pssenger, Mil/Express nd Goods mgnify the trffic jm prolem.

9 808 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) Solution In order to reduce the trffic jm t rotry 4, proposed flyover will e etween point 4 nd s shown in the key pln with green color. The tchometric trverse is run from oligtory points on the route survey 4, B, C, D, E nd. The trverse is plotted with limited oservtions i.e. distnces oserved y the tchometer. Computtion of trverse included using geomtic engineering: The excel sheet softwre is developed for eq.(1) to tulte the following results Tle 3. No. Pir of Trverse Sides Trverse Side lengths Computed dius Included Angle 1 4-B BC 199 m 187 m m Ang.4BC= BC CD 199 m 167 m 18.6 m Ang.BCD= CD DE 167 m 339 m m Ang.CDE= DE E 339 m 114 m m Ang.DE4= Tle 4. No. Pir of trverse Sides Trverse Side lengths Computed dius Included Angle 1 4-B BC 199 m 187 m m Ang.4BC= BC CD 199 m 167 m 18.6 m Ang.BCD= CD DE 167 m 339 m m Ang.CDE= DE E 339 m 114 m m Ang.DE4= Conclusion Thus knowing ll side lengths nd included ngles etween successive sides the required trverse of the fly over cn e plotted for further civil engineering design work. A new geometric concept is discussed to mke geometricl figures with less dt oservtion in the field. It finds wide ppliction in rod works plnning. The use of geomtic engineering softwre is demonstrted for plotting tchometric trverse where ngle oservtion in the field is completed omitted. Hence economy in rod work is justified. The modified pproch in ppliction of G.P.S. working rings economy on following heds: 1. Single stellite is used for the purpose. It rings sving on hiring chrges for the 3 spce stellite otherwise mndtory in current prctice.. The softwre to compute the results need to e modified ecuse overll cost of instlling the device will e considerly reduced. 3. ISO hs ssigned the tsk of development of new nd independent G.P.S. system nd its softwre to Ggn Augment Nvigtion Compny in our country. The concept discussed in this pper my e of gret use for the compny to develop the new GPS for the country.

10 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) eferences Mhjn, S.K. (1971). Explicit pproch to exterior orienttion. Journl of Surveying & Mpping Division, 97, Mhjn,S.K. (1969). A Comprtive Study of some Anlyticl eltive Orienttion Procedures in respect of precision nd efficiency. Thesis presented to University of oorkee, oorkee, Indi, in prtil fulfillment of the requirements for Mster Degree in Engineering. Mhjn, S.K. (197). Discussion on Spce esection from Collinerity Condition. Journl of Surveying & Mpping Division, 98. Mhjn, S.K. (197). Comprison of Anlyticl eltive Orienttion Methods. Journl of Surveying & Mpping Division, 98, Mhjn, S.K. (1971). Asolute Orienttion of Photogrmmetric Model. Journl of Surveying & Mpping Division, 97, Mhjn, S.K. (1974). A New method of Numericl eltive Orienttion of Photogrmmetric Model. Journl of Surveying & Mpping Division, 100, Mhjn, S.K. (1971). Evlution of some nlyticl procedures of plnimetric controlled trverse djustments. Journl of Institution of Engineers (Indi), 51, Mhjn, S.K. (1970). A Method of Tringultion with the help of Artificil Stellites. Journl of Institution of Engineers (Indi), 51, Mhjn, S.K. (008). Glol Tringultion Method. An Innovtive Mthemticl Approch Mgzine Invention Intelligence, Ntionl eserch Development Corportion, (A Government of Indi Enterprise). Mhjn, S.K. (008). Glol Mthemtics for Network Anlysis. DoMS I.I.T. oorkee guest lectures. Mhjn, S.K. (009). Glol Mthemtics Amendments in Fundmentl Mthemtics. Presented in 75th Pltinum Juilee Conference of the Indin Mthemticl Society, Klslingm University, Tmilndu, Indi. Mhjn, S.K. (01). Geomtic Applictions softwre in Civil Eng. Projects. Interntionl Journl of Advnced Civil Eng. Mhjn, S.K. (01). Gloemtic Science, e-book: Appendix A. The derivtion of eq.(1) Let the pir of given distnces form the two chords nd of circle which psses through the three points A, B nd C. Eq. of circle with centre (h, k) nd two chords nd, nd rdius is given y Eqution of the circle with s rdius: ( x h) ( y k) (1) Sustituting x nd y with the coordintes of points A, B nd O in Eq.(1) we get following equtions h k () ( h) k (3) From Eq.() nd (3) we get, h, nd k = ( / ) Consider Eq.(1), ( x h) ( y k) Differentiting w. r. to x, we get dy ( x h) ( y k) 0 or dx dy dx Sustituting the vlues of (h, k) in ove Eq. we get x y h k x dy (4) dx y ( / ) elow: the circle cn e determined s

11 810 S.M. Prsnn Kumr nd S.K. Mhjn / Procedi - Socil nd Behviorl Sciences 96 ( 013 ) Fig.9. Elements of glol tringle centre of the circle. The rdius of circle = sec Co. Therefore Sin / Or tn / ( / ) = m (5) which is the slope of the line AC with AB. We hve from Eq.(4) nd (5) / ( / ) / ( / ) ( / ) (6) On simplifiction nd re rrnging eqution (6) we get (7) of the circle cn e determined. Thus the orienttion of two chords nd within the circle whose rdius cn e determined from Eq.(7) is otined.