BC Punmia SURVEYING Vol 1 - By EasyEngineering.net

Downloaded From : www.EasyEngineering.net Downloaded From : www.EasyEngineering.net www.EasyEngineering.net **Note : Other Websites/Blogs Owners we requested you, Please do not Copy (or) Republish this Material. This copy is NOT FOR SALE. **Disclimers : EasyEngineering does not own this book/materials, neither created nor scanned. we provide the links which is already available on the internet. For any quarries, Disclaimer are requested to kindly contact us. We assured you we will do our best. We DO NOT SUPPORT PIRACY, this copy was provided for students who are financially troubled but deserving to learn. DownloadedThFraonmk:Ywowuwa.EnadsyGEondginBeleersinsg!.net Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net paras- wtaneja.blospo wwt.in .EasyEn(VOLUME I) ......_ Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net By Dr. B.C. PUNMIA Formerly, Professor and Head, Deptt. of Civil Engineering, & Dean, Faculty of Engineering M.B.M. Engineering College, Jodhpur Er. ASHOK KUMAR JAIN Director, Arihant Consultants, n Jodhpur ginee SIXTEENTH EDITION Dr. ARUN KUMAR JAIN ri(Thoroughly Revised and Enlarged) Assistant Professor M.B.M. Engineering College, Jodhpur ng.netLAXMI PUBLICATIONS (P) LTD BANGALORE e CHENNAI e COCHIN e GUWAHATI e HYDERABAD JALANDHAR e KOLKATA e LUCKNOW e MUMBAI e RANCHI e NEW DELHI INDIA e USA • GHANA e KENYA Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING-I © 1965, 1984, 2005 B.C. PUNMIA © 1994, 2005 ASHOK KUMAR JAIN, ARUN KUMAR JAIN Copyright © by Authors. wubuAi(nAponllaolmloankraewiygd(nffhoiudonttlrmshgmpe,eirrraneoanttsrch)deybaAryonavcnraetf,nddeo2yrlte0himrn1ceet2cevrf,laoituennnodwosific,ntppehsgaluheerratctphctrooroionofspsgnteyehisroci)si,og,f pmhafputnrteibrhycoalohripnclawdaasnerltriaticrio'ttoasnitlofe,imnntnphtahipeisyonelltbrteboomoecctoiorouskepsatphyiwlorieponintrrdghomu,lopacruueneesgrtcdttouty,hbra.sdeegItifoneopyrgsbeeo.troduamIrniiwninosoetsaahduiceorlcefrdnrwotorlroiiidmkesfeaevtn.aththocAleeesnupyypssuweustbueibtmlcmlihsihas,hhttaoeehecrrrertitscaor.oaClrnfnsorsscoptammiynturintittgtiehenhsedgt, Printed a n d b o u n d in India wTypeset at : Arihant Consultants, Jodhpur. w.RSepiFxrtiirhERnsttleEe:Epdv2rdeiti0niinto0tithno3:,nE:1:29d101i99t09i58o46,0n,5,1S,:S9iSe91xev6t9cee,8oen8Fnnt,ohtdhTuEEwrEtddeediilettifiinttooihtonnhnE:::Ed11di299ti0it86oi0o16n5n,,,:TE:1Rhi19gei9r9hpd90trh7i,En,REdtR:ideteipi2topri0nori0nnin6:t:t,:191:2197109829093,791,,8F, ,No21u109inr909tt98h2h9,, E,E21d2d09ii009ttii093oo0,,nn,2T::F0h111iifr990tte7,8ee65e2n,n,0ttFh1Thi1efEnt,Ehtd2dhiiE0ttiEi1doo2idnnt,iito:i:2no210n0:1903:192,914729808174 EE5U-0603·495-5URVEYING I (E)-PUN Price: ~ 4 9 5 . 0 0 asyEnewmtarwarLhendedouiishdsumvsrpsepoklitwoictterthnwesbssco,ueseetroairpkssbsftaetodtiarLwwrlheasivitteasrtaiyhaeicsrbitegeirncftioioeilifbtiaentonrthaecsyrmtada,cma/inDutonauayirndtnnisathstidiaccwonetbynhlnjaaheuiIdcisoentrsm/thinrotioebeveeruscoirirtgotanoooioihrmeeksrpgftsto.daprWoWetcnLalreaeomiianedzktonrebtaa.etrtinwhtsgaaaieieienloitnssrsetnsesweyso,aod:ouicrlrsiiTorfhsseWcmhite.teneheredmgNeoebpifeohinsuncifinebtoturhmtelsnherieetasfmtirhsnerhyoeanstewrhmyenrt soeioaa.pnrnntorkpTfodfdobuhvmrebtectimhhdlaaisiferaesysauethcoiaiwhaettoruaarrontrbtevhrhenldkeeaecooostocrraesfmhaonesmtnardnhmnnateoeoikgsearvpetaengleeumddatnrcotnyaoieohfittairzosirhcnoiaerdaetntputliisclhssorahyoaeatniaitpsntdloelompditnsnhreubac.taecWelyaarIttaneimiloemuidofabpatnbahsekbalinroeeoeltflye.rtrowoFwoariwfrmnueraardreatrietrhnnrshrafaegsaelewlnunrrpatar,mthiucecireeebtedtesiinsslav.vitdiswiotTatthheiiniheeeiirtynseshssr, stAlraulalxbdtmsreiadi dniaaeaprmmpieeaesarskor, isrtn,ragalfdofiengilmoitahsatioersksrw.'asNonoryorktoswaetrhiretvehirtscrtmeaadnamedrkaminrskagusrcktohhsfi.saatsnhddeVisiiicrbnlrgateeyismlolpree,ecrcUt,tuSiaavlPlle, opAotrwhmoepnareenrrndtsaay.m,oGewsonladeneddnbBmyeaollrrsk,lsiFcmierneewsneatdiloltnMoeLeddaxiinam,tihMPiseurbwcluoicrraykt,iaoTrnreisn,tihtiytes, ,- 10 Bangalore 080-26 75 69 30 044-24 3 4 47 26 0484-237 70 04, 405 13 03 ~ ~Hyderabad 0361-254 36 69, 2 5 1 3 8 81 040-27 55 53 83, 27 55 53 93 .,E ro Jalandhar 0 1 8 1 · 2 2 2 12 72 033-22 27 43 84 PUBliSHED IN INDIA BY 0522-220 99 16 ~ LAXMI PUBLICATIONS (P) LTD 022-24 9 1 5 4 1 5 , 24 92 78 69 113, GOLDEN HOUSE, OARYAGANJ, NEW D E l H I - 1 1 0 0 0 2 , INDIA - 0651-220 44 64 Telephone: 91-11·4353 2500, 4353 2501 Fax; 91-11-2325 2572, 4353 2528 C-8562/014/04 www.laxrnipublications.corn [email protected] P r i n t e d a t : Reoro lnrlirl 1t r l Mnmh;~i Downloaded From :

Downloaded From : www.EasyEngineering.net r ;I \\ ngineering.netTO MY FATHER Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net I I www.EasyEn Downloaded From : www.EasyEngineering.net

I Downloaded From : www.EasyEngineering.net I Preface ,'. This volwne is one of the two which offer a comprehensive course in those parts of theory and practice of Plane and Geodetic surveying that are most commonly used by civil engineers. and are required by the students taking examination in surveying for Degree. Diploma and A.M.I.E. The first volume covers in thirteen chapters the more common surveying operations. Each topic introduced is thoroughly describOd, the theory is rigorously developed, and. a ~rge DUIJ?ber of numerical examples are included to illustrate its application. General s~atements of important principles and methods are almost invariably given by practical illustrations. A large number of problems are available at the end of each chapter, to illustrate theory and practice and to enable the student to test his reading at differem stage~ of his srudies. Apan from illustrations of old and conventional instruments, emphasis has been placed on new or improved instruments both for ordinary as well as precise work. A good deal n of space has been given to instrumental adjustments with a thorough discussion of the geometrical principles in each case. g Metric system of units has been used throughout the text, and, wherever possible, inthe various formulae used in texc have been derived in metric units. However, since the cha~ge\\ over to metric system has still nor been fully implemented in all the engineering e;;;~:~~Jtirr:~ i;~ •JUr conntiy, a fe·,~- examples in F.P.S. system, hdxe ~!so beer: gi\\'C!\": eI should lik.e to express my thanks to M/s. Vickers Instruments Ltd. (successors to rM/s. Cooke, Troughton & Simm's), M/s. Wild Heerbrugg Ltd., M/s Hilger & Watci Ltd.. inand M/s. W.F. Stanley & Co. Ltd. for permitting me to use certain illustrations from their catalogues or providing special photographs. My thanks are also due to various Universities gand exami~g bodies of professional institution for pennitting me to reproduce some of .the questions from their examination papers. nlnspite of every care taken to check. the numerical work. some errors may remain. etand I shall be obliged for any intimation of theses readers may discover. JODHPUR B.C. PUNMIA 1st July, 1965 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net PREFACE TO THE THIRD EDITION In this edition, the subject-matter has been revised thoroughly and the chapters have been rearranged. Two new chapters on \"Simple Circular Curves' and 'Trigonometrical Levelling (plane)\" have been added. Latest Indian Standards on 'Scales', 'Chains' and 'Levelling Staff have been included. A two-colour plate on the folding type 4 m Levelling Staff, conforming wto IS 1779 : 1%1 has been given. In order to make the book more useful to the ~tudents appearing at A.M.l.E. Examination in Elementary Surveying, questions from the examination wpapers of Section A. from May 1962 to Nov. 1970 have been given Appendix 2. Account has been taken throughout o f the suggestions offered by the many users o f the book, and wgrateful acknowledgement is made to them. Futther suggestions will be greatly appreciated. .EJODHPUR 1st Feb.. 1972 asyPREFACE TO THE FOURTH EDITION EIn this edition, the subjec1-matter has been revised and updated. An appendix on n'Measurement of Distance by Electronic Methods' has been added. B.C. PUNMIA JODHPUR B.C. PUNMIA 15-10-1973 PREFACE TO THE FIFTH EDmON An Appenrli'~' In the Fifth Edition. the suhiect-matter ha!< ~n thnrnnQ:hly rP:vic:.,-1 on SI units bas been added. JODHPUR B.C. PUNMJA 25-4-1978 PREFACE TO THE SIXTH EDmON In the Sixth Edition o f the book, the subject-matter bas been thoroughly revised and updated. JODHPUR B.C. PUNMIA 2nd Jan., 1980 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net Jl( PREFACE TO THE NINTH EDITION In the Ninth Edition. the subject-matter has been revised and updated. JODHPUR B.C. PUNMIA 1st Nov., 1984 PREFACE TO THE TENTH EDITION In the Tenth Edition, the book has been completely rewritten, and all the diagrams have been redrawn. Many new articles and diagrams/illustrations have been added. New instruments, such as precise levels. precise theodolites, precise plane table equipment, automatic levels. new types of compasses and clinometers etc. have been introduced. Two chapters on 'Setting Out Works' and 'Special Instruments' bav~ been added at the end o f the book. Knowledge about special instruments, such as site square , transit-level, Brunton's universal pocket transit, mountain compass-transit, autom.nic le~~ls, etc. will be very much useful to the field engineers. Account has been taken througho~t of the suggestions offered by the many users o f the book, and grateful acknowledgement is made to them. Further suggestions will be greatly appreciated. n JODHPUR g lOth July, 1987 in PREFACE TO THE TWELFTH EDITION B.C. PUNMIA A.K. JAIN eIn the Twelfth Edition, the subject-matter has been revised and updated. erJOlJHPUR i30th March, 1990 ngPREFACE TO THE THIRTEENTH.EDITION B.C. PUNMIA .In the Thirteenth Edition of the book, the subject mauer has been thoroughly revisedA.K. JAIN nand updated. Many new articles and solved examples have ·been added. The entire book etbas been typeset using laser printer. The authors are thankful to Shri Moo! singb Galtlot for the fine laser typesetting done by him. JODHPUR B.C. PUNMIA 1 5 t h Aug. 1994 ASHOK K. JAJN ARUN K. JAIN Downloaded From : www.EasyEngineering.net

fDl!ownloaded From : www.EasyEngineering.net i- I:! SI X !! PREFACE T O T i l E SIXTEENTH EDITION In !he Sixteenth Edition, !he subject matter has been thoroughly revised, updated and rearranged. In each chapter, many new articles have been added. ·Three new Chapters have been added at !he end o f !he book : Chapter 22 on 'Tacheomelric Surveying'. Chapter 13 on 'Electronic Theodolites' and Chapter 24 on 'Electro-magnetic Disrance Measurement (EDM)'. All !he diagrams have been redrawn using computer graphics and !he book has wbeen computer type-set in bigger fonnat keeping in pace with the modern trend. Account has been taken throughout o f !he suggestions offered by many users o f !he book and grateful wacknowledgement is made to !hem. The authors are thankful to Shri M.S. Gahlot for !he fine Laser type setting done by him. The Authors are also thankful Shri R.K. Gupta. wManaging Director Laxmi Publications. for laking keen interest in publication of !he book and bringing it out nicely and quickly. .EJodhpur Mabaveer Jayanti asyEnlsi July, 2005 B.C. PUNMIA ASHOK K. JAIN ARUN K. JAIN .I ___ Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net Contents CHAYI'ER I FUNDAMENTAL DEFINITIONS AND CONCEPTS 1.1. SURV~YING : OBJECT I 1.2. I PRIMARY DIVISIONS OF SURVEY 3 4 1.3. CLASSIFiCATION s 1.4. PRINCIPLES OF SURVEYING 8 1.5. UNITS OF MEASUREMENTS .8 10 1.6. PLANS AND MAPS II 12 1.7. SCALES 18 19 1.8. PLAIN SCALE 20 21 1.9. DIAGONAL SCALE 22 1.10. THE VERNIER '1:1 '1:1 1.11. MICROMETER MICROSCOPES 28 29 1.12 SCALE OF CHORDS 3() 1.13 ERROR DUE TO USE OF WRONG SCALE 31 1.14. SHRUNK SCALE 37 1.15. SURVEYING - CHARACI'ER OF WORK 37 38 CIIAYI'ER2 ACCURACY AND ERRORS 46 49 2.1.GENERAL 2.2. so 2.3.SOURCESOFERRORSso 2.4. KINDS OF ERRORS S4 n 2..5. S7 2.6.TIIEORY OF PROBABILITY60 g CHAPTER 70 i 3.1.ACCURACY IN SURVEYING PERMISSmLE ERROR 70 n3.2. e3.3. 8S e3.5. r3.6. ss i3.7. n3.8. 8S 3.9. g3.10. .3.11. ~~~ net4.1. ERRORS IN COMPUI'ED RESULTS 3 LINEAR MEASUREMENTS DIFFERENT METHODS DIRECT MEASUREMENTS INSTRUMENTS FOR CHAINING RA..'IJG!t-;G OL-; S0RVEY U.NJ;.s CIWNING MEASUREMENT OF LENGfH WITH TilE HELP OF A TAPE ERROR DUE TO INCORRECI' CHAJN. CHAINING ON UNEVEN OR SLOPING GROUND ERRORS IN CHAlNING TAPE CORRECTIONS DEGREE OF ACCURACY IN CHAINING PRECISE UNEAR MEASUREMENTS 4 CHAIN SURVEYING CHAIN TRIANGULATION 4.2. SURVEY STATIONS 4.3. SURVEY LINES \"' Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net xn _;{4 LOCATING GROUND FEATURES : OFFSETS 87 FIELD BOOK 92 4.5. FIELD WORK 94 INSTRUMENTS FOR SEITING OUT RIGJIT ANGLES 9S 4.6. BASIC PROBLEMS IN CHAINING 98 OBSTACLES IN CHAINING 100 4.7. lOS 4.8. wCROSS STAFF SURVEY 106 ~. PLO'ITING A CHAIN SURVEY 109 110 4.10. w5 THE COMPASS 116 / 4.11. wBEAIUNGS 118 .ETHE SURVEYOR'S COMPASS 120 VCHAPTER INTRODUCfiON 124 5.1. ANGLES !25 5.2. aMAGNETIC DECUNATIONAND 5.3. 127 5.4. m E 'I'HEORY OF MAGNETIC COMPASS 133 5.5. sERRORS S.6. THE PRISMATIC COMPASS 137 5.1. 137 5.8. y6 THE THEODOLITE 141 WILD 8 3 PRECISION COMPASS 142 /~R EGENERAL 144 ISO 6.1. THE ESSENTIALS Ill 6.2. ATTRACTION ISS 6.3. nDEFINITIONSLOCAL 6.4. IN COMPASS SURVEY j 6.l. { 6.6. OF THE TRANSIT THEODOLITE 6.7. 6.8. AND TERMS 6.9. TEMPORARY ADJUSTMENTS PROCEDURE MEASUREMENT OF HORlZONTAL ANGLES GENERAL MEASUREMENT OF VERTICAL ANGLES MISCELLANEOUS OPERATIONS WITH THEODOLITE RElATIONS FUNDAMENTAL LINES AND DESIRED SOURCES OF ERROR IN TI!EODOLITE WORK ll6 CHAPTER 7 TRAVERSE SURVEYING 161 161 , !!'l'TP0!\"!U':'T!0!'J' 162 162 7.2. CHAIN TRAVERSING NEEDLE METIIOD 164 7.3. 16l 7.4. CHAIN AND COMPASS TRAVERSING FREE OR LOOSE 167 7.5. 168 7.6. TRAVERSING BY FAST NEEDLE METHOD 169 7.7. TRAVERSING BY DIRECT OBSERVATION OF ANGLES 171 7.8. AND TAPE 172 7.9. LOCATING DETAILS WITH TRANSIT 7.10. 177 7.11. CHECKS IN CLOSED TRAVERSE 7.12. PLOTIING A TRAVERSE SURVEY CONSECUTlVE CO-ORDINATES LATmJDE AND DEPARTURE CLOSING ERROR BALANCING TilE TRAVERSE DEGREE OF ACCURACY IN TRAVERSING CHAPTER 8 OMITIED MEASUREMENTS AND DEPARTURE 179 8.1. CONSECUTIVE CO-ORDINATES : LATITUDE ISO 8.2. OMITfED MEASUREMENTS Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net XIII 8.3. CASE I ' BEARING. OR LENGTH, OR BEARING 181 SIDE OMIITED 182 8.4. AND LENGTH OF ONE ONE SIDE AND BEARING OF ANOTF.HR SIDE OMmED 182 8.l. CASE D : LENGTH OF 182 8.6. 183 8.7. CASE m ' LENGTHS OF TWO SIDES OMIITED CASE 19l CASE IV : BEARING OF TWO SIDES OMmED -196 II, m, IV : WHEN THE AFFECTED SIDES ARE NOT ADJACENT 197 201 ~R 9 LEVELLING 204 DEANIDONS 211 9.1. 213 METHODS OF LEVELLING 21l _fl 216 LEVELLING INSTRUMENTS 216 9.3. 222 226 9.4. LEVELLING STAFF 230 9.5. THE SURVEYING TELESCOPE 233 23\"? 79.6. TEMPORARY ADJUSTMENTS OF' A LEVEL 238 240 THEORY OF D!RECT LEVELLING (SPIRIT LEVELING) 243 244 9.8. DIFFERENTIAL LEVELLING 244 9.9. HAND SIGNALS DURING OBSERVATIONS 2\"48 2l2 '-)kf'( BOOKING AND REDUCING LEVELS 257 BACKSIGIITS AND FORESimiTS 9.11.BALANCING '-\" ~ CURVATURE AND REFRAcriON 2S9 9.13. 260 9.14.RECIPROCALLEVELLING 264 266 9.15.PROALELEVELLING (LONGITUDINAL SECfiONJNG) 267 n 9.16. CROSS-SECTIONING 271 9.17. 273 g 9.18. LEVELLING PROBLEMS 27S i 9.19. 27l n9.20. 276 ~ ee9.21. ERRORS IN LEVELLING m DEGREE OF PRECISION 278 THE LEVEL TUBE OF BUBBLE LEVELLING r10.1. TIJBE SENSITIVENESS i10.2. n10.3. 10.4. BAROMETRIC HYPSOMETRY gIO.S. 10 CONTOURING .10.6. UE.i>it:RA.i.. n_ / CONTOUR INTERVAL CHARAcrERISTICS OF CONTOURS et11.1. METHODS OF LOCATING CONTOURS INTERPOLATION OF COtiTOURS CONTOUR GRADIENT 10~7. USES OF CONTOUR MAPS \\.QHAPTER 11 PLANE TABLE-SURVEYING GENERAL ACCESSORIES 11.2. WORKING OPERATIONS 11.3. PRECISE PLANE TABLE EQUIPMENT i. METHODS (SYSTEMS) OF PLANE TADLING 6 . INTERSECTION (GRAPHIC TRIANGULATION) TRAVERSING RESECITON Downloaded From : www.EasyEngineering.net

~ D', ownloaded From : www.EasyEngineering.net \"\"' ~' 11.8. THE THREE-POINT PROBLEM:- . 279 11.9 TWO POINT PROBLEM 285 11.10. ERRORS IN PLANE TABLING 287 ~ 11.11. ADVANTAGES AND DISADVANTAGES OF PLANE TABLING 289 12.2. r/CIIAPI'ER 12 291 12.3. 292 292 ~ 292 2'11 vz.5. w~ 298 w12.7. 302 CALCULATION O F AREA 304 305 12.1. GENERAL 315 GENERAL METHODS OF DETERMINING AREAS 315 319 AREAS COMPIJTED BY SUB-OMSION IJ'IITO TRIANGLES 321 322 12.8. 322 327 w_/ -~--9. 332 ._,.£HAYfER AREAS FROM OFFSETS TO A BASE LINE : OFFSETS AT REGULAR INTERVALS OFFSETS AT IRREGUlAR INTERVALS AREA BY DOUBLE MERIDIAN DISTANCES $ .E~13.1 AREA BY CO-ORDINATES AREA COMPUTED FROM MAP MEASUREMENTS AREA 13 a~THTEHE BY PLANIMETER MEASUREMENT OF VOLUME .JYI'/ s.\\....J¥5. GENERAL MEASUREMENT yE__!)<'8. FROM CROSS-SECTIONS PRISMOIDAL FORMULA TRAPEZOIDAL FORMULA (AVERAGE END AREA METHOD) nCIIAPI'ER 14 THE PRISMOIDAL CORRECTION 13.6. THE CURVATURE CORRECTION VOLUME FROM SPOT LEVELS VOLUME FROM CONTOUR PLAN MINOR INSTRUMENTS 14.1. HAND LEVEL 337 14.2. 338 14.3. ABNEY CLINOMETER (ABNEY LEVEL) 340 14.4. (l'ANGENT 341 14.5. INDIAN PATIERN CLINOMETER CLINOMETER) 341 14.6. 342 BUREL HAND LEVEL 343 L'f.l. 343 DE LISLE'S CLINOMETER 344 14.8. 345 14.9. FOOT-RULE CLINOMETER 14.10. L . c . l i ...V I ' ' I LT.I1f\\1 IHJ\\.CI=.K CIIAPI'ER FENNEL'S CLINOMETER THE PANTAGRAPH THE SEXTANT 15 TRIGONOMETRICAL LEVELLING 15.1. INTRODUCTION 349 15.2. 349 15.3. BASE OF THE OBJECT ACCESSIBLf: 352 355 15.4. BASE OF THE OBJECT INACCESSIBLE : 'INSTRUMENT STATIONS IN 359 361 15.5. THE SAME VERTICAL PLANE AS THE ELEVATED OBJECT 15.6. BASE OF THE OBJECT INACCESSIBLE : INSTRUMENT STATIONS NOT IN THE SAME VERTICAL PLANE AS 1HE ELEVATED OBJECT DETERMINATION OF HEIGHf OF AN ELEVATED OBJECT ABOVE THE GROUND WHEN ITS BASE AND TOP ARE VISIBLE BUT NOT ACCESSIBLE DETERMINATION OF ELEVATION OF AN OBJECT FROM ANGLES OF ELEVATION FROM THREE INSTRUMENT STATIONS IN ONE LINE Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net \"' CHAPI'ER 16 PERMANENT ADJUSTMENTS O F LEVELS 16.1. INTRODUCriON 365 16.2. 365 16.3. ADUSTMENTS OF DUMPY LEVEL 372 16.4. 373 ADJUSTMENT OF TILTING U:VEL ADJUSTMENTS OF WYE LEVEL CHAPI'ER 17 PRECISE LEVELLING 17.1. INTRODUCfiON 377 17.2. THE PRECISE LEVEL 377 17.3. 378 17.4. WILD N-3 PRECISION LEVEL 378 17.S. 319 17.6. THE COOKE S-550 PRECISE LEVEL 319 17.7. 380 17.8. ENGINEER'S PRECISE LEVEL (FENNEL) 380 381 17.9. FENNEL'S FINE PRECISION LEVEL 382 17.10. PRECISE LEVELLING STAFF CHAPI'ER FIELD PROCEDURE FOR PRECISE LEVELLING FlEW NOTES DAILY ADJUSTMENTS OF PRECISE LEVEL 18 PERMANENT ADJUSTMENTS O F THEODOLITE 18.1. GENERAL 385 18.2.ADJUSTMENTOFPlATELEVEL 386 18.3. 386 18.4.ADJUSTMENTOFLINEOFSIGHT 388 18.5.ADJUSTMENT 388 ADJUSTMENT OF THE HORIZONTAL AXIS CIIAPI'ER VERTICAL 391 OF ALTITUDE LEVEL AND INDEX FRAME 392 n 19.1. 392 19.2. 393 g 19.3. 394 19.4. 395 in19.5. 396 19.6. e10\"\" 398 eCIIAPI'ER 398 r20.1. 398 i20.2. 400 n20.3. 400 20.4. 403 g20.5. 404 .20.6. n20.7. 405 CHAPI'ER 405 et21. 1. 406 19 PRECISE THEODOLITES 408 408 INTRODUCTION WATIS MICROPTIC THEOOOLITE NO. 1. FENNEL'S PRECISE THEODOUTE WILD T-2 THEODOLITE THE TAVISTOCK THEODOLITE THE WIW T-3 PRECISION THEODOLITE THE WU .n T~ TJNJVF-~SAL THEOOOUJ'f. 20 S E T I I N G OUT WORKS INTRODUCTION CONTROLS FOR SETilNG OUT HORIZONTAL CONTROL VERTICAL CONTROL SETIING OUT IN VERTICAL DIRECTION POSITIONING OF STRUCTURE SETTING OUT FOUNDATION TRENCHES OF BUILDINGS 21 SPECIAL INSTRUMENTS INTRODUCfiON 21.2. THE SITE SQUARE 21.3. AUTOMATIC OR AUTOSET LEVEL 21.4. TRANSIT-LEVEL 21.5. SPECIAL COMPASSES Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net XVI 21.6. BRUNTON UNIVERSAL POCKET TRANSIT 409 ~~ MOUNTAIN COMPASS-TRANSIT 410 22.1. 22 TACHEOMETRIC SURVEYING 411 wPRINCIPLE 411 22.2. GENERAL 412 DISTANCE 413 22Jr INCLINED 416 ~: wDISTANCE 417 INSTRUMENTS OF TACHEOMETRIC MEASUREMENT 418 .J'-6. DIFFERENT SYSTEMS wPRINCIPLE OF SUBTENSE (OR MOVABLE HAIR) 431 22.7. OF ~ADIA METHOD 434 22.8. AND ELEVATION FORMULAE FOR STAFF VERTICAL ~37 .HORIZONTAL BASE SUBTENSE MEASUREMENTS ~ SIGIIT 438 EHOLDING THE STAFF 439 22.10. AND ELEVATION FORMULAE FOR STAFF NORMAL 442 446 22.11. THE ANALLACfiC LENS 449 aSTADIA 452 22.12. METHOD : 453 dl3. VERTICAL LI\\SE OBSERVATIONS sTilE 22.14. yREDUCI10N 22.15. ETHEMETHODSOF READING TilE STAFF 22.16. FIELD WORK 22.17. nWILD'S RDS REDUCI10NMETHOD TANGENTIAL OF STADIA NOTFS SPECIAL INSTRUMENTS AliTO-REDUCfiON TACHEOMETER (HAMMER-FENNEL) TACHEOME.TER 22.18. THE EWING STADI-ALTIMETER (WATI'S) 455 22.19. ERRORS IN STADIA SURVEYING 455 22.20. 456 EFFECf OF ERRORS IN STADIA TACHEOMETRY, DUE TO MANIPULATION AND SIGHTING. • CHAPTER 23 ELECTRONIC THEODOLITES 23.1. INTRODUCTION 465 23.2. WILD T-1000 'TIJEOMAT' 465 23.3. WILD T-2000 THEOMAT 467 :?.-1 ',V!LD T :C•X S :!-I£0:\\-~'.:· -tiu CHAPrER 24 ELECTRO-MAGNETIC DISTANCE MEASUREMENT (EDM) 24.1. INTRODUCTION 471 24.2. ELECTROMAGNETIC WAVES 471 24.3. MODULATION 415 24.4. TYPES OF EDM INSTRUMENTS 476 24.5. THE GEODIMETER 478 24.6. THE TELLUROMETER 479 24.7. WILD 'DISTOMATS' 481 24.8. TOTAL STATION 488 APPENDIX 493 INDEX 531 Downloaded From : www.EasyEngineering.net

f Downloaded From : www.EasyEngineering.net I []] ~ Fundamental Defmitions and Concepts 1bdoaogfisne.iifif1rrvndser.eetecmpnalqtoiitSoaunohintpieeUnhrilSaeSLeeetRrruhdamvearenVvatmvwaiidetnoeEtilesiioylntcaeuiYthinnhsnslre,ugeIfgivaNsrorescaerpiGemetssirhistepot:eyaiqeanonntsOcut.ifightcSibdBersI.roteit,haJftduofTEenaaetcahnlrCso1hneeeao0Tfdnaotoaariegtflpnhftlnioepcvakdlslleeubbiuiencvndylsrteaaeodvettnmsseioimontoyrhoenitnienhenfaseigaoneenswnsxfgwsagttuonhesiiomturnenthkfhroteesv,eeodfderrbyiieetanjrorsisesdeengpttccaaltgeatobttbwcuteniltormoviooesfrermqhd,tkoiuewsynispi.an.grhioanegdLisdscnipierhgeteovisdioci(evkniintlesiiill)sSwnilnmhgabto(eioosiylaf)rdesewupeptaartoresolhesesllimseladnufbwiieemanSlstnsiideetseihnSchdtonohtmnhnieo,npededofeaakdirsaennduoublioemripSoaswevenvt.maarlgeteaanieuTdttocnilgohnoaeieSrr.saen ngineiepbsanahrrriroeodljauigeemlcesdtstvaTedbhsasreueuent,icrdchvdatkehblenyateuoessiprwlmsdlwwtalireninaeundegrtcege.esrdreuemrsateocunas.fpddpemrseltyuuqhinrseuvtaierncteybodoiepnnsoniugrsgerrtvrcaiagiteksipayoehtsdniy.aodnowBvouaiesfttnfcholhtaorhegleneamenpoetsdluhsiat,senessurgiasrnrahviolnoerudoyumnailnddeadsg.nst.yibmAeaPnaspr1dahaestaschctstreeieaacnsrnaaewlsilmnooypre,frikdsese.peivopnaenAgrrreoiyfndgtliee.rnereeebnrsissogtn,heuignesnm,.edepialrnTliranieinhneesegsss, eringaptrbVhnereaedodttrwujteciecgceiettardIinanlodmnettdohassiuyeostrfahvmprnoeoauecrynipsieniztrnstoesgansbr.aeteeaanrareltaelg,ladutinhvhisdmseeuotnaawe.lsnaalheysrcvoueeewasrrre.s,empoTensrohnehnsotelseaywnntoohehodfoojbreryicilzbzerooyncnngootltmamahillsoeuaadprnailsrsasetlnuaineron.vehfceseoy,AsvriezhroolaStpfincclhlaaattunhollr,eesospoerpncroo:i:riipmoneantalsnsssop.:emdVpieasrlreaaeornwtttihhncseeauurlrbshesmdopemirqa5eiaurZtthapaeontonnecdttlsleaysyosl..'· .net1motthh.f2eeet.ttpeshuoseP)lrTaRfhraeIbeacMeeratixenhAaiogsrfRtthihYstshiosiesmshDioeiasmMwrntaehlSgeroasibIlnstOlaharlatNetyenhsSasssntphptOhehh0eeaF.err3noqo4iuiSddatUhtpooaiResrtfriVacaroelEenfvcYatuo.xirlitusvsItefibdoeynqwssue4u,a2ritf.onha9reec5igael,lleekcniealtgvoxetmihtrshyeetor(fee1ils2rei.irm,S7eRge5pnue6otll.aal7atro5irivft0ieeawsxtmihosaiect_tr'hhr{ee1rsih2lsd.e,7ina1Tmeo3arh.er8murr0esha0r,.l Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING I ' to the plumb line. The intersection o f such l a surface with a plaue passing through the centre of the earth will form a line continuous around the earth. The portion o f such a line is known as 'level line' and the circle defined by the iD[ersection is known as 'great circle'. Thus in Fig. 1.1, the distance be- tween rwo points P and Q is the length 0 f the arc o f the great circle passing through wrbese poin£S 3nd is evidently somewhat more than the chord intercepted by the arc. wConsider three points P, Q and R IFig. I . I ) and three level lines passing through wti1ese points. The surface within the triangle PQR so formed is a curved surface and .rhP lin~!' fonning irs sides are arcs of great Ecircles. The figure is a spherical triangle. TI1e angles p, q and r o f the spherical auiangle are somewhat more than correspond- sing angles p', q' and r' of the plane triangle. If the points are far away, the difference ywill be considerable. If the points are nearer, the difference will be negligible. As ro whether the surveyor must regard.Ahe eanh's surface as curved or may regardFIG. 1.1 Eit is as plane depends upon the character and magnitude of the survey, and upon the nprecision required. Thus, primarily, surveying can be divided into two classes (I) Plane Surveying (2) deodetic Surveying. Plllne surveying is that type o f surveying in which the mean surface o f the earth ; , considered as a plane and the spheroidal shape is neglected. A l l triangles formed by survey lines are considered as plane triangles. The level line is considered as straight and :1!1 plumb lines are considered parallel. fn everyd~y life we ar-:- ~\"nc~rned with small portions o f earth's surface and the above assumptions seem to be reasonable in light o f the fact that the length o f an arc 12 kilometres long lying in the earth's surface is only I em greater than the subtended chord and further that the difference between the sum o f the •ngles in a plane triangle and the sum o f those in a spherical triangle is only one second for • triongle at the earth's surface having an area o f 195 sq. km. Geodetic surveying is that type of surveying in which the shape o f the earth is taken into account All lines lying in the surface are curved lines and the triangles are spherical triangles. It, therefore, involves spherical trigonomeuy. All geodetic surveys include work o f larger magnitude and high degree o f precision. The object o f geodetic survey is to determine the prfdse position on Ihe suiface o f the earth, o f a system o f widely distanr points which fonn corurol stations 10 which surveys o f less precision may be referred. Downloaded From : www.EasyEngineering.net

I FUNDAMENTAL DEFINITIONS AND CONCEPTS Downloaded From : www.EasyEngineering.net 3 l 1.3. CLASSIFICATION I Surveys may be classified under headings which define the uses or purpose o f the ~ resulting maps. \\ (A) CLASSIFICATION BASED UPON THE NATURE O F THE FIELD SURVEY ' (1) Land Surveying (1) TopofPYJPhical Surveys : This consists of horizontal and vertical location of certain points by linear and angular measurements and is made to determine the nanual feanues o f a country such as rivers, streams, lakes, woods, hills, etc., and such artificial features as roads, railways, canals, towns and villages. Cud~tral surveys are made incident to the fixing of property (it) Surveys : Cadastral lines, the calculation o f land area, or the transfer o f land property from one owner to another. They are also made to frx the boundaries o f municipalities and o f State and Federal jurisdictions. (iii) Cily Surveying : They are made in connection with the construction o f streets. water supply systems, sewers and other works. (2) Marine o r Hydrographic Survey. Marine or hydrographic survey deals with bndies o f water for pwpose o f navigation, water supply, harbour works o r for the deiermination o f mean sea level. The work consists in measurement o f discharge o f streams, making topographic survey o f shores and banks, taking and locating soundings to determine the depth o f water and observing the fluctuations of the otean tide. n the surface of the earth. This consists in observations to the heavenly bndies such as the g(B) (3) Astronomical Survey. The astronomical survey offers the surveyor means of determining the absolutei(1) Engineering Survey. This is undertaken for the determination of quantities or to nafford sufficient data for the designing of engineering .works such as roads and reservoirs, or those connected with sewage disposal or water supply. e(2) 1'-.:filiU:a.r.)' .S:ari1 ~J'. This is i.lStd for determining pubts of slrategic i!l1p'.Jrtance. location o f any point or the absolute location and direction o f any line on sun or any fixed star. CLASSIFICATION BASED ON THE OBJECT O F SURVEY e(3) Mine Survey. This is used for the exploring -mineral wealth. r(4) Geological Survey. This is used for determining different strata in the earth's icrust. n(5) Archaeological ·Survey. This is used for unearthing relics of antiquity. g(C) CLASSIFICATIONBASED ON INSTRUMENTS USED .An alternative classification may be based upon the instruments or methods employed, nthe chief typeS being : e(1) t(2) Chain survey Theodolite survey (3) Traverse survey (4) Triangulatiqn survey !5) Tacheo111etric survey (6) Plane table· survey Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net r 4 SURVEYING fJ' (7) Phorogrammetric survey i: and (8) Aerial survey. ! www.EomsabLfrccafeoeacstmtleuohedrto.PhadteaTT(Tesa1tralhhhr)yneeeep(ldFeoaarpiofignnsueQoLft.ltdniasond.tvcttibas1vwetaemhA.ret2oePiyneo)tpnyhnpatoresae·nosiolmlidiotatnrhitefpoptieQfsvnlrereaerisn<owplcn'otofppiilalp(ifool;ntlersueitteti,nrshhtfipeteeuoosrusnuiebppasncnsyonothecsidnnoerv,matfosewscneatPhhtaanRoisesct,huhabbrernpceeeedaoftmgehnssrriseUetQeotianbInouVtvetcnneaceedsdryalf.oienrpodoocuouTamfnisbnthsdeehteewdsmorthuwpedflillotlcidtoyohshhrttoerabodefpninehdsxcofyaieoinlvnoloogleotfconPsafwQtptahteiotllhnehrdaefegecnaraebfednroysletyalwhfsltobeeumiovebewrreteeveianeenamsynctpsgoupieoenreasgecfdissim1tixuoirsoerameeendnrcdese:.tt The book mainly deals with the principles and methods of the above types. 1.4. PRINCIPLES O F SURVEYING ap p I rs. yA Sf-T-A E90• p Fp I b v na 6 a' a a A ' ,~R )A (a) (b) (c) (d) (e) AG. L2. LOCATION OF A POINT. (a) Distances PR and QR can be measured and point R can be plotted by swmgmg to which PQ has been plotted. The principle is very much the two arcs to suthre,evisna.mt?e scale used in r.hain and lengths PS (b) A mdpeeefarinpsuienrngeddi.cduelTatahrielsR.pSoincat nRbecandrothpepnedbeonplothtteedreufesrinengcesetlinsequaPrQe. This principle are and SR for is used . pepairnotihginnlecetripR((RlbIcefyQ)) iPsiTIsmnhpeaevlarotenhetristdyseimdsotmmeafnaeeuscitactuhehhorepedrQdr,uoRstbterwyhdaeiactnthmoiddnreiasatntnorhansrne\"caaotenanrsgfngiglgueoaPll-aenmRloipoemPrnaaoQesntutdrRraariinccnQtdacgolRalrynt.hinoaesbrrTeterhmubimnsymeotehetpnsaoroLmsdilnuuerctKeaiiisopdsnunleorueawsondieisdfndgbtuupfrsoitotaerhindneagtn·vligeendRl,riesyPttariQR·sanePvRc:ueeQp.'relsoniTPtsnathiQnegviddes., w\"ork .. either by protracting (e) Angle RQP and distance PR are measured and point R is plotted This principle, used arc from P or pJoned trigonometrically. an angle and siws inogfingminanor utility. in lTaversing , Downloaded From : www.EasyEngineering.net

r- Downloaded From : www.EasyEngineering.net ; FUNDAMENTAL DEPINITIONS AND CONCEPTS arlbiensyleathtaiovkPreiFQinwiggenslise.sttavala1fi.tnf.i2soFrtneriu(asgbdm).i/o.ne,2gnf(.tcpa)(loSbliyiam)nntisderl.aesrpt(alCrdybe),olsinesFcnshaiitgedns.dera1tihtn.lhse2goro(puctbrh)gieenhascneuidpPselded(idaa)ngtodorrfaemioptlhlrrsuedessintteorvanaertirybettieicletsahpliepnirrhiiptnvercieiglinrephtcviltcieepalsllolienofsgpf.lRtoarnfiAgeidso. enhtmoweomnrietinahezistonruniiPrcnteaQagdll levelling. J fwmmemirxhieranotoghotlrnheorsiedt(Tmu2satthdo)rneeadawsvnWpesidatrteiohroscfteort.shkncthheoidiIgneenthtgtdcrrereu.oirestllfvairnTpieolvagrrhsmeenserecdpycirsaipiiwdlnnooreehCncosaio.cstapheellleeniosMesnstefiiaotnoliwbmfsoeoristnprfuokooclarorliovrnlcenoteagsetwytrrreioaerndibldonglr,,ipssuthoshtwliiw1innhsuftghessirtiwchstctmhehaar.eyanaskopeiittnlshhsagymenesnrteitotwnehmoboiesprreer.wegecovseoofwetonarndoktbctruelooitlnuslditchhtnr,eecpoedooxlisniapnbtcaprttycsnooouldilmnlabwelbySustoosllerarkatpuginaorrndftenenrcaoiittnmshtoegoeref end. l!l 1.5. UNITS O F MEASUREMENTS in plane surveying: Vertical distance There are four kinds of measurements used nIIijg ot1h9fe5m6beatt3Lhsr.iieiccnueulnainnirHtietasomorrfieiznammosneeuItaanarssedluusirar.aee, nmsA,gfeeclneebc,ttoo,rtohdatfinendnidgntihssttmaonaecnttehrdiecishSuamtsna4dne.rwtdreaeedrsltdlhsasVansoedorffticincWeaanleBtfiiomrgaiohtnetittsgsrhlweesa.e.snrydePstreuMiomsree,dat.sowurThtehaislebelAeinTctat1rb.o1(ldeIunsgcditivi1aoe.)n2s, I . Horiwntal distance 2. i.r, n\\ e~1 British Units \"1 e I·t and 1.3 give the conversion factors . r' leel -'A-B- L-E- 1- ·.1- -B-A-S-IC- U--N-IT-S- O- -F -L-E-NG- -T-H- ! in';! yards Metric Ullits 10 millimetres = I centimetre ~ 12 inches =I fool gl I i IV .A.:iiiiOii~(l,;;:, J..;-::;;:;,:l:~ ! .I 10 chains yaro =I ; ] 10 decimetres n\"k = I metre = I rod. pole or perch I ei 4 poles = 1 chain (66 fee!) !w metres = I decametre I t= 66feei = I furlong 10 decametres = I hectometre 8 furlongs = I mile 10 hecwmetres = 1 kilometre = I nautical mile (lntemationa\\) >;.. 100 links =I chain ! 1852 meues I I 6 feel =I fathom I 120 fathoms =I cable length I 6080 feet =I nautical miie I I Downloaded From : www.EasyEngineering.net

Downlo6aded From : www.EasyEngineering.net SURVEYING TABLE I.Z CONVERSION FACTORS (Mnres, yards, feet and irrch2s) Metns Y<Uds Feet IncMs I 1.0936 3.2808 0.9144 I 3 0.3048 I O.OZS4 0.3333 0.0278 0.0833 w I'Kilometres 39.3701 36 12 I . Miles w III I w1.852 . I1.6093 TABLE 1.3 CONVERSION FACTORS (/(jfomerres, NauJical miles and Miles) Nautiud miles EBasic units of area. The units of measurements of area are sq. metres, sq. decimetres, 0.539% 0.6214 hectares and sq. kilometres. Table 1.4 gives the units o f area bolh in metric as well asI 1.1508 aBritish sysiems. Tables 1.5 and i.6 gives !he conversion factors.0.869 I sTABLE 1.4 BASIC UNITS OF AEEA I yEt44 sq. inches f n9 sq. feet l ~ -~ l BriJWJ Unils Metric U11ils = I sq. f001 100 sq. millimerres = sq. cenrimeue = I sq. Yard 100 sq. centimetres=- sq. decimerre 30} sq. yards = I sq. rod, pole or perch 100 sq. decimeues = sq. merre 40 sq. rods = I rood 100 sq. metres are or I sq. 100 ares decametre = 1 acre 100 hectares 4 roods hectare or = 1 sq. mile 1 ~q = I sq. chain hcctc:o.J<:l<~ 640 acr.s = I acre = I sq. kilometre 484 sq. yards to sq. chains l TABLE 1.5 CONVERSION FACTORS i (Sq. metres. Sq. y<Uds. Sq. feet and Sq. inches) ! Sq.\"'\"\"' Sq. y<Uds Sq. feet Sq. i11ches j I 1.196 10.7639 1550 0.8361 I 9 1296 I' 0.0929 I 0.00065 0.111 I 144 I 0.00077 0.0069 I I Downloaded From : www.EasyEngineering.net

FUND~AL DEFINJ\"i10NS AND CONCEPTS Downloaded From : www.EasyEngineering.net 7 TABLE 1.6 CONVERSION FACTORS (Ares, Acres and sq. yords) Ares Acres Sq. yards I 0.0247 119.6 I 40.469 I 4840 I 0.0084 0.00021 I I' I sq. mile = 640 acres= 258.999 hectares I I acre = 10 sq. chains I are = I00 sq. metres Basic units of volume. The units of measurements of volumes are cubic decimetre.c:. and cubic metres. Table I . 7 gives the basic units o f measurement o f volumes holh in metric as well as British units. Tables 1.8 and 1.9 give ! h e conversion factors. TABLE 1.7 BASIC UNITS OF VOLUME ~f -1British Unils Metric Units 1728 cu. inches== cu. foot 1000 cu. millimwes cu. centime1res 27 cu. 'feet cu. yards 1000 cu. cemimettes cu. <lecimenes ng Cu. metres 1000 cu. decimelres cu. melres iI : n0.7645 TABLE 1.8 CONVERSION FACTORS Gallons (Imp.) e0.00455 (Ql. metres. Ql. y<Uds and Imp. galloiU) 219.969 l 168.178 Cu. yards I I 1.308 I l 0.00595 i•' eriCu. metres nI i g1233.48 .n0.00455 et1.000028 TABLE 1.9. CONVERSION FACTORS (Oibic merres, Acre feet, Imp. Galloru and Kilolitres) Acrejeet Ga/lom (lmp.J Kilolitres 0.99997 0.000811 219.969 1233.45 0.00455 I 271327 I 0.00000369 I 0.000811 219.976 -----· Basic units o f angular measure. An angle is the difference in directions of two intersecting lines. The radiml is the unit of plane angle. The radian is !he angle between two radii o f a circle which cuts-off on the circumference of an arc equal in length to the radius. There are lhree popular syslemS o f angular measurements: Downloaded From : www.EasyEngineering.net

.Downloaded From : www.EasyEngineering.net . 8 SURVEYING I (a) Sexagesi111f1] System (degrees of arc) r. (minutes of arc) wcircumference = 360• 1 circumference =60' (seconds of arc) I degree = 60\" 1 minute wcentigrad· (b) Centesi111111 System w1 circumference = 4008 (grads) grad = 100' (centigrades) .hour EasyEoschuotohrmuvererpsyuiTptnasahygtriesottsneinmsesatxnroaudimfgsmeiitensnhminutmeettoseraspWtlloayrlosaeyrtliusdotsg.enermd,adMtuhioianesrteedcawescnitdoartoeecmsnlcyipoomlrmedaut1iyesnegsd=tayanstb6odtilen0em'stnhUaiaisvnsriie(gtssegayedatacsiiovtonenaSnimni.dtlgaa.stbelmsHeo, ofo·rwiGenteirmveftaeahevrt)i,so. uBdrsruyietsiantientmEo, urfIaoanncpddieilai.tymTaonhisndet= 100cc (centi-centigrads) n1bbeabbIlsiIaerh.eyyn6elrooet.rwhswp.roh.selnermapPt.iATnhsrbLtaesheohOalcAseeglccape,nrNuhaonlaearufstrSpatvneeruhheed·per1ttidsfhAosrciaesepcNoseootaeenaapDtngrpnrhrrdrgtatoeoahasepojMputfe'.estithcchgohrAihtrteenciohasroPoeupnnSmmnpihrssfaiaayaecpapwpcwsaace,tselraierh·ttplhmhihlicreowmaoosehdnufw.paia,ttsyrhetetaohvhsmgpeueeebemrrtenen,oatappejasdetpllrtuhraaiaciesnoernitgtaienioybafdv,r,oriltesedirtrohteootondiednrcdm.uraiaysaslsaawotpcIosmdnanrhilht.esieoipsotopralrinaHlnsziiapn.zscconoloeaeamewnlsnseatmeea,aiasv,nlaruedeolrrmlnpvf,oaleshawltytsseanhiiophnneneniaccclgereere,tefwsephaimorttttihaehfucanseehrpieasetnhssateiiuecarssedattofralsnaelsrcubecc,eordyenpfniaornnseccnaetovsoerasefounrnplctvcotlttaeaheaeourdnddneerr (c) Hours System = 24h (hours). = 60m (minutes o f time) 1.7. SCALES oSosduncnisacthlatethnheceaTi((ess12.hg))gertir1shooOOeueuaninnmrnnfeededidax,.=eeuepdsnm1teSuhi0ntccardhataoeolmtennfiiaotsslcteehoattsnec1hnfu~g.artviu,hpbeTnleaeyihotnveesinedstrcreroy.eptthifpyrseTedrpmesihesevspiteesnaalaantsonesnttrfcusdaertareisesonmcboopdaynmre,l·oeenesftttethhhnimeewsaetnsrahedppfcofolsaolaloelidlrnlsmoeeisw,dnetcbauiaennpmelnagcllnuaerbengsdmesmirntbowreeeoeateirhtprftrhheor'oseedmfscsmeoescsmtcroaar:radermaerlseteseei.pvspeootuononnfndriditsatnshoicgnemtgiooedfgnigr.slsoretcoaunauTnnglnchedthed.e. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net f FUNDAMENTAL DEFINITIONS AND CONCEP'TS 9 I representative fraction (abbreviated as R.F.) can be very easily found for a given engineer's scale. For example, if the scale is I em = 50 m R.F. \"\"' \",7o-1'--,o~\"' = I 5000. f~ scale. The above two types of scales are also known as numerical scales. is to draw on the plan a graphical (3) An alternative way of representing the scale distance corresponding to convenient A graph~cal scale is a line sub-divided into plan !lI uniTsnohitatasi·lg~iVooiIsffe.dwrlrheahne~wygc.nctphu,lrsaacnioratneleowsrrtiehllsaemurleastgpshrraoiinluifwsknadttyh.poserobpdsehroaeretwuirosnendoartoenlpyaaafptlaeelnrrdsusahrthvrifeeneywkds.misytaaeHpnasocr.swe,sevtcehare,n nwnerical scales may if a graphical scale be found accurately. ~ CrcodfehifhenporoiraosetiihecsslriseeenrTdn21igotth..tooeferdmStCCybhmcaheheapbooolt.ypeooossltsscooeieaottbcftlnoeeeaaaedwmsMairmslc.relcseeapomaTnprnlneetaa:ioslbmlsetlcl(eneaaaIttrbl)erge1eedess..1tcha0infeesolTenergchosueieuvoaossgssemerahdsfreioiytnstolhslaoomerctwywoouctinlhhnotmsiiagmrpcietashlamtpeedtisnwnottohnoatefprhwesleocgtimeattetthnlhisanen.ocpesgasarelaTgewlchoeiilnnerlecrleaulroiwrlpnabeslrhseeledyirslceichplmsuaihtunhlsioitteenan,huadnageltrdiayoinnnd0ndwi.bc2svetono5aa(nbf2nrseif)comoirtedhulmlteesoohrf.wefarssotueimmmodervnxaeelttlretyeehinnssset.t 'J :'· n TABLE 1.10 g Type or purpose of surve i(a} Topographic Survey I Stale R.F. n1. Building sites e2. Town plaMing schemes. em = 10 m or less 'ffiY1 S or less ereservoirs etc. em = 50 m to lOOm It 11 : . ____ ! . ' - • ' - · -~ . C:l'l ~- '(\" 'ltYI ~ soo.rto lOCOO I1 ri4. Small scale topographic maps em = 0.25 km to 2.5 km < 1 ¥ w 2 1 ) n(bJ Catkistral maps ; em = 5 m to 0.5 km ;J im gfcJ Geograplu·cal maps i em = 5 km to 160 km .nfdJ U:mgiwdinnl seaio11s 250100' w I I etI. Horizontal scale II EOOOO II 1 to 1 !I 500 5000 11 500000 to 16000000 em = 10m to 200 m 1t t 10i50 to 20000 2. Venical scale em = 1m to 2 m I1 100 to 200 ;' 1 (e) 0os.J-.5ection.s I 1 em = lmto2m I1 <Both horizomal and vertical 100 ID 200 scales equal) Downloaded From : www.EasyEngineering.net

Download1e0d From : www.EasyEngineering.net SURVEYING Types of Scales Scales may be classified as follows I . Plain· scale 2. Diagonal scale 3. Vernier scale 4. Scale of cbords. 1.8. PLAIN SCALE A plain scale is one on which it is possible to measure two dimensions as units and lengths, metres and decimetres, miles and furlongs, etc. Example 1.1. ConstrucJ a pillin scale 1 em to 3 metres and slww on it wC<lnstructWn : if;1~~~~:~wl~~~w(~;;rr-r T·r·r--r··r-1 ' Ivision imo 10 equal parts, each 10 only, such 47 metres. . •reading I metre. Place zero Eof the_ scale between lhe sub- divided parts and lhe undivided apart and mark lhe scale as shown in Fig. 1.3. To take 47 metres, place one leg of•01• 0• 2• 0• •30• 4•0• 5- 0 slhe divider at 40 and lhe olher at 7, ·as shown in Fig. 1.3. SCale 1 c m = 3 m yIndian Standard on plain scales FIG. 1.3 PLAIN SCALE. IS : 1491-1959 has recommended six different plain scales in metric units used by I Eengineers, architects and sorveyors. The scale designations along wilh lheir R.F. are given nin the table below: DesiRrUJtlon S<ok R.F. A 1. Full size I ' B- I T c 2. SO em to a metre I 3. 40 em to a metre D 2 ' 4. 20 em 10 a metre nI S. 10 em to a metre I 6. 5 em to a metre 5 7. 2 em to a metre I 8. 1 em to a metre Tii I 20 I 51i I TOO E 9. S mm to a metre I 200 F 10. 2 mm to a metre I ----- - 11. I mm to a metre 500 -- 12. O.S nun w a metre I - TiiOO I ~QQ9 Downloaded From : www.EasyEngineering.net

FUNDAMI!i'ITAL DEFINmONS AND CONCEPTS Downloaded From : www.EasyEngineering11.net 1.9. DIAGONAL SCALE 1 On a diagoual scale. it is possible to measure lhree dimensions such as metres. de<!imetres and centimetres; units, tenlhs and hundredlhs; yards, feet and inches etc. A short Jenglh I is divided into a number of parts by using lhe principle of similar ! triangles in which like sides are proportioual. For example let a \" ij sbort Jenglh PQ be divided into 10 parts (Fig. 1.4). At Q draw a line QR perpendicular to PQ i and of any convenient Ienglh. Divide it into ten equal parts. Join lhe diagonal PR. From each of lhe divisions, I, 2, 3 etc., draw lines parallel to PQ to cut lhe 4 diagonal in corresponding points I, 2, 3 etc., lhus dividing lhe diagonal 5J - - - - j 5 into I0 equal parts. 6t..---.16 Thus. t~~I8 1-1 represents .!.. PQ 99 represents 2-2 10 Pa 1. PQ 10 fo9-9 represents FIG. 1.4 PQ etc. Example 1.2 ConstruCI a diagonal scale 1 cm=3 metres to read metres and decimetres and show on thal 33.3 metres. Construction : Take 20 em Jenglh and divide it into 6 equal pans, each pan representing 10 metres. Sub-divide lhe first left band part into 10 divisions, each representing I metre. At the n left of lhe first sub-division erect a perpendicular of any suitable .lenglh (say 5 em) and divide it into 10 equal parts and draw lhrough lhese parts lines parallel to lhe scale. Sub-divide glhe top parallel line into ten divisions (each representing 1 metre) and join lhese diagonally ito lhe corresponding sub-divisions on lhe first parallel line as shown in Fig. 1.5 wbere na distance of 33.3 metres has been marked. e1.0 0.9 0.8 ej 0.7 0.6 l r0.5 0.4 i0.3 I ~~~~:••m n0.2 0.1 !rgln~0.0 ·l .nl~ Scale1cm=3m I el FIG. 1.5 DIAGONAL SCALE. tIndian_ Standard on diagonal scales IS : 1562-1962 recommends four diagonal scales A, B. C and D. as sbown in lhe table below : Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING ~~ I2. De~ignation R.F. Graduated ltng!h A I ! ISO em w 3. T I. I 100iXXl wI Ic 100 c~ I8 2. I 5<XXXJ w3. I I . 2500) I ! 100Xil' .'I!. I ED I 50 om 2. 51iXii'f a3. I I 23000 sy1.10. THE VERNIER The vernier, invented in 1631 by Pierre Vernier, is a device for measuring the fracrionalI Epart of one of the smallest divisions of a graduated scale. It usually consists of a small100iXXl nauxiliary scale which slides along side the main scale. The principle of vernier is based 2. I 150 em 8liD I I I I 4li'ii' on the fact that the eye can perceive wilhow strain and with considerable precision when two graduations coincide to jonn one continuous straight line. The vernier carries an index mark which forms the zero of the vernier. I f the graduations of the rp.ain scaJe are numbered in one direction only. the vernier used is called a single vernier, extending in one direction. I f the graduations of the main scale are numbered in both the directions, the vernier used is called double vernier, extending in both the directions, having its index mark in the middle. The division.~t C'f the vernier are either j~1st a little smal!f':- r-r :- litt!r 12rgcr th:m the divisions o f the main scale. The finen~ss o f reading or least count o f the vernier is equal to the difference between the smallest division on the main scale and smallest division on the vernier. Whether single or double, a vernier can primarily be divided imo the following two classes : (a) Direct Vernier (b) Retrograde Vernier. (a) Direct Vernier A direct vernier is the one which extends or increases in the same direction as that o f the main scale and in which the smallest division on the vernier is shoner than the smallest division on the main scale. It is so consrrucred that (n - 1) divisions of the main scale are equal in length of n divisions o f the vernier. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 13 FUNDAMENTAL DEFINmONS AND CONCEPTS Let s = Value o f one smallest division on main scale v =.Value o f one smallest division ·on the vernier. I n = Number o f divisions on the vernier. Since a length o f (n - I) divisions of main scale is equal to n divisions o f vernier, I we have nv = ( n - 1) s l Thus, 1)V= ! division by ( n- - S i -. ~ Least count= s - v = s - -n -n-1 s =-ns. I the least count (L.C.) can be found by dividing the value o f one main scale the total number of divisions on the vernier. ; ,:; , , , dv ! ! ! l OJ 01l ! ! ! lv! ! ! l I (\"I' '1II1,,·\"'' \"tll\" I II\"'II' t \"'I(I II IIIII s 0 II II II I 12 I 21 14. 13 ~ (a) (b) ._-.-;!': n1gineI ering•i .l n~ i ~, l 1 et' FIG. 1.6 DIRECT VERNIER READING TO 0.01. Fig. 1.6(a} shows a direct vernier in which 9 parts of the main scale divisions coincide with 10 parts o f the vernier. The total number of the divisions on the vernier are 10 and the value o f one main scale division is 0.1. The least count o f the vernier is lherefore, ~·~ = 0.01. The reading on the vernier [Fig. 1.6(b)) is 12.56. Fig. 1.7 (a) shows a double vernier (direct type) in which the main scale is figured in both the directions and the vernier also extends to both the sides of the index mark. L... :. c ; ~l.· ~~II,\\'I i, 'Ii'J,i',UIiiI ~IlI 1\" 11I ' I II \\'iII liill''''''f 70 80 90 ( 3 0 6U IU\\ (b) (a) FIG. ! . 7. DOUBLE VERNIER (DIRECI). The 10 spaces on. either half of the Vernier are equivalent to '9 scale divisions and hence least count is ~ = ~ =0.1. The· left-hand vernier is used in conjunction with the upper figures on the main scale (those sloping to the left) and the right-hand vernier is used 1 in conjunction with the lower figures on the scale (those sloping to the rigbt). Thus, in Fig. 1.7 (b), the reading on the left vernier is 40.6 and on the rigbi vernier is 59.4. l 1 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYIN9 14 (b) Retrograde Vernier A retrograde vernier is the one which extends or increases in opposite direction as thal o f the main scale and in which rhe smallest division o f the vernier is longer than the smallest division on the main scale. It is so · constructed that (n + 1) divisions of the wThe least count main scale are equal in length o f n divisions o f the vernier. Thus. we have. for Ibis case or v =n -+-1s n nv=(n+ l)s : which is the same as before. wFig. 1.8 (a) illustrates a retrograde vernier in which 11 pans of the main scale wdivisions coincide with 10 divisions of the vernier. The value of one smallest division on Ithe main scale is 0.1 and lb~ number of division on the vernier are. 10. Therefore, the .least' counr is = ~-~ = 0.01. The reading on the vernier [Fig.I.8 (b)] is 13.34. = v - s =( nl -+. -t ] s - s = ns , ·r EI\" ,alo ' IOj- s··!····~~~~~r;+1•1•1•1••1•1•1 y(•) EFIG. 1.8 RETROGRADE VERNIER. .. 1 )'1111111'~\"nIIrI !OJ 11!' I1\"11\"1111\"1 niSPECIAL FORMS OF VERNIERS ..:' 14 13 n w close The Extended Vernier. It may happen that the divisions on the main scale are very - exact and it would then be difficult, if the vernier were o f normal length, to judge the used. graduation where coincidence occurred. In this case. an extended vernier may be ' He-r'=' r?_ '7 _ ! ) ri!Yl\"'k-.\"1s :~-:: i.L .... .:. ~..: ..u..: .:.:'-[ual 'o ;1 lhvisruns on [fie vernier. ~ so that nv = ( 2 n - 1) s - Of V 2n-l = 1 2 - 1\\ l -jS =--S I \" ~ n, n i' The difference between two main scale spaces and one vernier space = 2s - v i 2n- l s : = 2s - - n s = -n = least count. -- The extended vernier is, therefore. equivalent to a simple direct vernier to which only every second graduation is engraved. The extended vernier is regularly employed in •- We asuonomical sextant. Fig. 1. 9 shows an extended vernier. l r has 6 spaces on the vernier f equal to 11 spaces o f the main scale each o f 1o . The least count is therefore = f,. degree = 10'. J Downloaded From : www.EasyEngineering.net ~ ~ ~~ j 1

FUNDAMENTAL DEFINmONS AND CONCEPTS Downloaded From : www.EasyEngineeri1n5 g.net rI f160 60J I I, I II II I II I '1 , 30 0 30 , I I ,I , ,I I I II I II I II 110 5 0 5 10 I (•) I r 30 I I o~ I I 30 ~ II I II I I ' 'I I IJ I \\Ill 11111111111 ljl II I I lfr!j I 5 10 15 10 5 0 ; (b) ~ r r ' 'l60 30 601 0 30 Jl .r--'{ I )I I .I I II ) ) I l I' .j. III I I j )II I II I II I1 ~I I) 10 5 0 5 10 15 (<) \\ FIG. 1.9 EXTENDED VERNIER . •j The reading on the vernier illustrated in Fig. 1.9(b) -is 3 ' 20' and that in Fig. 1.9(c) ni~~ g• ; i is 2°40'. ~ In the case o f astronomical sextant, the vernier generally provided is o f extended l type having 60 spaces equal to 119 spaces of the main scale, each of 10'. the least count ' in~' ' being ~ minutes or 10 seconds. ' eother extreme division in !hE\" s::f!ie direction w the centre. The Double Folded Vernier. The double folded vernier is employed where the length o f the corresponding double vernier would be so great as to make it impracticable. This e~ Fig. 1.10 shows double folded vernier in which 10 divisions of vernier are equal type o f vernier is sometimes used in compasses having the zero in Ihe middle o f the length. The full length o f vernier is employed for reading angles in either direction. The r-l to 9 ! divisions of the main scale '<or 20 vernier divisions= 19 main scale divisions). The il n\"l i' -~ vernier is read 'from the index towards either o f the extreme divisions and then from the gi •f .net-~ 30leastcountofthe vernier is !!qual to !n._ = _2_0!_ degrees = 3'. For motion w the right. the · :~ -~ J (•) (b) ~~ FIG. 1.10 DOUBLE-FOLDED VERNIER. ~ j 1 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING I 16 a0tvotertnot6hi0ee3r0(coiesranttrzreeetah.rdeo)Tflhreaoeftmt trehex0eatdreitcnomegni3ttyr0oen. aantStdhitmehtehilvearenrirlgynhf,iretorfmeoxriltlr3uem0smtoriatatitytoendtahnetoidnrittghFhheeigtn.leefxfr1ott,.rm1e0mth3iet(0yb)vaetotrisntitheh1ere12li6es'0ft1r8e(e'aoxdrttroezfmerotrihomtey) right and 247' 42' to the left. Verniers to Circular Scales wwcHIunlsieenndoFcmiegt.eTo. thelec1resai.r1sca1teubtlcoac(.voraeu)F,nsiecgtxat.hal=eem1ss.p1sil1icnenas=l(eaao)3f,i0vsa'v(1breg3i)rer0natsyide=hurosoa1wtf'e.swdseutwrrteovoefy3otiyr0np'gilcianainlnedasatrrrutrhasmcenaeglnevetmsas.leunseVutsecorhnof ifeanrsds=otuah3br0eeloedoaodnllisiroteetchse,texvtseveenexrnsrtnaiivenieertsrlsy.., w.Eas10 yEn(A) Graduated to 30°: Reading to 1'..... (B) Graduated to 20' : Reading to 30\" FIG. 1.11. VERNIERS TO CIRCULAR SCALES. m ~1g. 1.11 (b), the scale is graduated to 20 minutes, and the number o f vernier divisions are 40 . Hence, least count~ s i n = 20'140 = 0.5' = 30\". Thus, in Fig. 1.11 (~), the clockwise angle reading (inner row) is 342' 30\\ + 05' = 342' 35' and counter clockwise angle reading (outer row) is 17' 0' + 26' = 17' 26'. Similarly. in Fig. 1.11 (b), the clockwise angle reading (inner row) is 4 9 ' 40' + 10'30\" = 4 9 ' 50' 30\" and the counter, clockwise angle (outer row) is 130' 00'+ 9' 30\" = 130' 09' 30\". In both the cases. 1he vernier is always read in rhe same direction as the scale. Examples on Design o f Verniers Example 1.3. Design a vernier for a theodolite circle divided inro degrees and half degrees to read up to 30\". .; Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net FUNDAMENTAL DEFINmONS AND CONCEPTS ii Solution I Leasi Count=:!n. ; S = 30' • L .C. = 30\" = 6300- minutes ~ .. 30 30 or n =60. 60=• I Fifty-nine such primary divisions should be taken for the length o f the vernier scale and then divided into 60 ·parts for a direct vernier. Example 1.4 Design a vernier for a theodolite circle divided imo degrees and one-tlzirJ degrees to read to 20 \". \" Solution. iI L . C . s ; s = 1' 2 0 ' ; L.C. = 20\" = ~ minutes =; 3= 20 20 ' -oo=•~ or I I = 60 I, Fifty-nine divisions should be taken for the length of the vernier scale and divide-d ~ into 60 parts for a direct vernier. Example 1.5. The value o f che smallest division o f circle o f a repeating cheodolite is 10'. Design a suitable vernier to read up to flY'. Solution L.C.= ~; s = 10' ; L.C. = 10\" = !~ minutes n .. g Taite 59 such primary divisions from the main scale10 10 i Example 1.6. The circle of a theodolite is divided inro60=• nDesign a suitable decimal vernier to read up to 0.005°. eSolution or n = 60 eL.C. ri0.005 and divide it into 60 pans. degrees and 114 o f a degree. Il ngor =s- ; s = ~' ; L.C. = 0.005' n 1 .Take 49 such primary divisions from lb.e main scale and divide it into 50 parts =I- n-I· 4 nfor the vernier. . el Example 1.7 Design an extended vernier for an Abney level to to read up to JO •.n=I=50 The main circle is divided into degrees. tSolution 4 X 0.005 Ij L . C . = !n. . ; s = l 0 ; L.C. = 10' 1 10 =;I or n=6 60 ~ 1 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net ... ' SURVEYING 20 ····· '• 3. Measuremem o f a n angle with E. the scale of chords I . Let the angle EAD be measured. On the line AD. measur~ AB = chord of F.,. 60~ from the scale of chords. B 2. With A as cenrre and AB as FIG. L l 6 MEASUREMENT OF AN ANGLE wradius. draw :m ·arc to cur line AE in WITII T i l E SCALE OF CHORDS . . F. w •3. With the help of dividers take the chord distance BF and measure it on scale of chords to get the value of the wangle ij, .1.13 ERROR DUE TO USE OF WRONG SCALE EIf the! length of a line existing on a plan or a map is determined by meansA D m~suremem with a wrong scale. the length so obtained will be incorrect. The []Jle acorn!ci lt!ngrh of the line is given by the relation. syCorrect length = R . F . oiff wrong scale x measured length. of R . F . o correct scale or ESimilarly. if the area of a map or plan is calculated with the help of using a wrong nscale. rhe correct area is given by Correct area = .' R . F. ooffcworrornegctssccaalele V x calculated area. \\! R . F. 1 1 Example 1.8. A surveyor measured the distance between rwo points 011 the plan drawn ro a scale o f I em = .JO m and tile result was 468 m. Later, however, he discovered that hi! used a scale o f 1 em = 20m. Find the true distance between the points. Solution Measured length =468 m R.F. of wrong scale used tt ' 2 0 X 100 = 2000 R.F. of correct scale 40 X 100 4000 Correct length ' I /2000 '! x 468 = 936 m. =ll/4000} ' AltemaJive Solution Map distance between two points measured with a scale of 1 em to 20 m = ~~ = 23.4 em Acrual scale of the plan is I em = 40 m :. True distance between the poinrs = 23.4 x 40 = 936 m Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net I FUNDAMENTAL DEFINITIONS AND CONCEPTS \" I 1.14. SHRUNK SCALE r I f a graphical scale is not drawn on the plan and the sheet on which the plan .~ is drawn shrinks due to variations in the atmospheric conditions, it becomes essential to find the shrunk scale of the plan. Let the original scale (i.e. I em= x m) or its R.F. be known (stated on the sheet). The distance between any two known points on the plan can be measured with the help of the stated scale (i.e. I em = x m) and this length can be compared with the acrual distance between the two points. The shrinkage ratio or shrinkage factor is then equal io the ratio of the shrunk length to the actual length. The shrunk scale is then given by \"Shrunk scale = shri11kage factor x origilli11 scale.\" For example, if the shrinkage factor is equal to :~ and if the original scale is 1 , the ~ (i.e. I em= 16m). 161500 shrunk scale will have a R.F = :~ x 1; 00 = Example 1.9. The area o f the plan o f an old survey plolled to a scale o f /0 metres w 1 em measures now as 100.2 sq. em as found by a planimeter. I11e plan is found to have sllru11k so that a line originally 10 em long now measures 9. 7 em only. Find (i) the shrunk scale, (ii) true area o f the survey. n,~ Shrinkage factor = ~·~ = 0.97 g.I I I J. True scale R.F. - 10 x 100 - 1000 i II nR.F. of shrunk scale= 0.97 x 1000 = 1030.93 e(it) Present length of 9.7 em is equivalent to 10 em original length. Solution (t) Present length of 9.7 em is equivalent to 10 em original length. l ;.? ePresent area of 100.2 sq. em is equivalent to r' '0 J' x 100.2 sq. em= 106.49 sq. em= original area on plan. I in·'l Scale of plan is I em = 10 m gI ~i .map drawn to a scale of 100 m to 1 em. Calculate its area in l1ectares. If the plo! n:·~ is re-drawn on a topo sheet ro a scale of 1 km to 1 em. what will be its area on ethe. topo sheel ? Also determille tlze R.F. of the scale of tile villa!{e map as well as Area of the survey = 106.49 (10)' = 10649 sq. m. Example 1.10. A rectangular plot of land measures 20 em x 30 em on a village tSolution I (i) Village map : on the topo sheet. 1 em on map= 100 m on the ground I em' on m a p = (100) 2 m2 on the ground. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING !8 Take eleven spaces o f the main scale and divide it into 6 spaces uJ ·the vernier. l . l l . MICROMETER MICROSCOPES Generally, verniers are used when the finest reading to be taken is riot less than 20'' or in some:: exceptional cases up to 10\". The micrometer microscope is a device which enables a measurement ro be taken to a srilJ finer degree of accuracy. Micromerer microscopes · generally provided in geodetic theodolites can read to 1\" and estimate to 0.2\" or 0.1 \". The micrometer microscope consists of a small low-powered microscope with an object glass, an eye-piece and diaphragm which is capable of delicately controlled movemem at wright angles to the longitudinal axis of the tube. Fig. 1.12 shows a typical micrometer and one tbnn o f the field of view in taking a reading is shown in Fig. 1.13. The circle win Fig. .1.13 is divided into lO miri.utes divisions. The micrometer has an objective Jens close to lhe circle graduations. It fonns an enlarged image o f the circle near the micrometer weye-piece, which further enlarges the image. One pair of wires mounted on a movable frame is also in the image plane. The frame and the wires can be moved left and right by a micrometer screw drum. One complete revolution of the gradu.:ted drum moves the .Evertical wires across o1:1e division or 10' of lhe circle . The graduated drum is divided imo 10 large divisions (each of I') and each o f the large divisions into 6 small ones aof I 0\" each. Fractional parts of a revolution of the drum, corresponding to fractional parts sof a division on the horizontal circle, may be read on the graduated drum against an index mark fined to the side. yThe approximate reading is determined from the position of the specially marked V-notch. EIn the illustration of Fig. 1.13 (a), the circle reading is between 32' 20' and 32' 30' and nthe double wire index is on the notch. Tum the drum until the nearest division seems ro be midway between the rwo vertical hairs and note the reading on the graduated drum, as s h o w n i n F i g . 1.13 (b) w h e r e the r e a d i n g is 6' 10\". The c o m p l e t e reading is 3 2 ' 26' 10\". The object of using two closely spaced parallel wires instead o f a single wire , -/- , 1. ObJective ·-+ , , 2.t., i';.,;c.;, ' · ' / ''<1// . / ///_~ :.- '/,;.~ ' / / . . 3. Drum ~: 4. Index 1.11 · :\"·1 J ;.·:~·~~:;?-. .' (a) : lmnmml• t -+~~~b!.klM.,~!J,'J.J\"'~''Y,-.;'///h'P', .32 I t 3 2 2 Plan I FIG. 1.12. MICROMETER FIG. 1.13 1 MICROSCOPE. ! Downloaded From : www.EasyEngineering.net

r FUNDAMENTAL DEFINITIONS AND CONCEPTS ,.Downloaded From : www.EasyEngineering.net is to. increast; t~ precision o f centering over graduations. 1.12 SCALE OF CHORDS A scale o f chords is used to measure an angle or to set-off an angle, and is marked either on a recmngular protractor or on an ordinary box wood scale. l 1. Construction or a chord scale I . Draw a quadrant ABC. making AB l = BC. Prolong AB to D. making AD = AC. I 2. Divide arc AC in nine equal parts, each part representing 10'. '' \\ l . ..' 3. With A as the centre, describe arc '' '-J ' ' ''''' . si from each o f the divisions, cutting ABD into points marked 10' , 2 0 ' , ... 9 0 ' . ''' ' ' ''' ' ~ ·.;; 4. Sub-divide each of these parts, i f ' ' ''' required, by first subdividing each division ' ~ .' ' ''' ' ''•' o f arc AC, and then draw arcs with A as centre. as in step 3. B _' _D_' 10\" 20\" ao• 40\" so· so· 1o• so· 90\" 5. Complete the scale as shown in ~ Fig. 1.14. II should be noted that the arc ~n mark. For example, the distance between A to 40' mark on the scale is eqnal to the gn througll the 6ff' division will always pass FIG. !.14. CONSTRUCTION OF A CHORD SCALE. r: through the point 8 (since the chord o f -'~;~ 6 0 ' is always equal to radius AB). The i) I. Draw a line AD, and on that I~; chord of 40'. distance from A to any mark on the scale is eqnal to the chord o f the angle o f thar 1 nmark AB. = chord of 60' from the scale e ~·~ of chords. e) 2. With A as centre and AB as radius, draw an arc. 2. Construction o f angles 3 0 ' a n d 8 0 ' with the scale of chords. (Fig. 1.15) j ri3. With B as centre and radius n·'l equal to chord of 30' (i.e. distance from o• to 3 0 ' on the scale o f chords) draw J gan arc to cut the previous arc in E. ~ .'~ n:j I eso·radius equal to chord of tfrom o· to so· on the scale of chords) Join AE. Then L EAB = 3 0 '. 4. Siniilarly, with B as centre and eo· (i.e .• distance BD 2 draw an arc to em previous arc in F. FIG. !.15. CONSTRUCTION OF AN ANGLE WITH TilE SCALE OF CHORDS. I Join A and F. Then L F A B = SO'. 1 ! Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYlNG I 22 The plo1 measures 20 em ~ 30 em i.e. 600 em2 on lhe map. Area of plol =600 x 104 =6 x 106 m' =600 hectares. (il) Topo sheet w(iii) R.F. of lhe scale of village map 1 km2 is represemed by 1 em' or (1000 x 1000) m' is represemed by I em' . . 6 x 106 m2 is represented by . ~~- 1 . A-- x 6 x 106 -= 6 cm2 wR.F. of lhe scale of topo sheer w1.15. SURVEYING - CHARACTER OF WORK 1 100 X 100 = J0000 IThe .1. E i2. 3. a1. I 1 X 1000 X !00 = 100000 work of a surveyor may be divided inlo lhree distincl pans Field work instrumenrs. Office work Care and adjusbnenl of lhe F l E W WORK sThe field work consisrs of lhe measuremem of angles and dis1ances and lhe keeping ! yof a record of whal has been done in lhe form of field notes. Some of lhe operations Ewhich a surveyor has IO do in !he field work are as follows : i 1. Esrablishing srations and bench marks as points of reference and lhus 10 esrablish ! nIa system of horizontal and vertical· control. ··s'Ij ~ 2. Measuring dislance along lhe angles between lhe survey lines. ~ ~ 3. Locating derails of lhe survey wilh respecl lo lhe srations and lines between srations. f derails sucb as ·boundary lines, streeiS, roads, buildings, streams, bridges and olher narural l or anificial features of the area surveyed. J 4. Giving lines and elevations (or setting our lines and esrablishing grades) for a ~ greal vanety of construction work such as that for buildings boundaries, roads, culverts. ;1 bridges. sewers and waler supply schemes. I 5. Derermining elevalions (or heighiS) of some existing points or esrablishing points at given elevations. .\\I 6. Surveying comours of land areas (topographic surveying) in which the field work involve both horizonral and vertical control. 7. Carrying out miscellaneous operations, such as j ti) Esrablishing parallel lines and perpendiculars I (iz) Taking measurements m inacessible points. (iir) Surveying paSI lhe obsracles. and carrying on a grea1 variery of similar field work thar is based on geometric or trigonometric principles. 8. Making observations on the sun or a star to determine the meridian. latirude or longirude. or to deterntine lhe local time. 1-, Downloaded From : www.EasyEngineering.net

I FUNDAMENTAL DEANmONS AND CONCEPTS Downloaded From : www.EasyEnginee2r3ing.net Field notes. Field nmes are written records of field work made at the time work is done. It is obvious that, no matter how carc:fully the field measurements are made. the survey as. a whole may be valueless if some of those measurements are not recorded or if any ambiguiry exists as to lhe meaning of lhe records. The competency of the surveyor's planning and his knowledge of the work are reflected in the field record more than in any other element of surveying. The field notes should be legiSie. concise and comprehensive. written in clear. plain letters and figures. Following are some general imponant rules .for note-keepers : I . Record directly in lhe field book as observations are made. 2. Use a sharp 2H or 3H pencil. Never use soft pencil or ink. I 3. Follow a consistem simple sryle of writing. with a title of the 4. Use a liberal number of carefully executed sketches. equipmem used. 5. Make the nares for each day's work on the survey complete survey, dare,. weather conditions, personnel of the crew, and list of 6. Never erase. If a mistake is made, rule one line through the incorrect value i and record the correction above the mistake. ! 7. Sign lhe notes daily. The field notes may be divided into three parts : s 1. Numerical values. These include lhe records of all measurements such as lengths of lines and offsets, sraff readings (or levels) and angles or directions. All significant figures should be recorded. If a lenglh is measured 10 lhe nearest 0.01 m. it should be so recorded: for example, 342.30 m and not 342.3 m. Record angles as os• 06' 20\". using a1 leaSI two digits for each pan of the angle. nI 2. Sketches. Sketches are made as records of outlines, relative locations and topographic gfeatures. Sketches are almost never made to scale. If measurements are put directly on the skerches. make it clear where they belong. Always make a skerch when it will help ito settle beyond question any doubt which otherwise might arise in the interpretation of nnares. Make sketches large, open and clear. e3. Explanatory notes. The object of the explanatory notes is to make clear rha! ewhich is not perfectly evident from numerals and skerches. and to record such information concerning important features of the ground covered and the work done as might be of rpossible use later. in2. OmCE WORK The office work of a surveyor consist of g1. Drafting .2. Computing n3. Designing j eThe drafting mainly consists of preparations of lhe plans and secrions (or plouing tmeasurements to some scale) and to prepare topographic maps. The computing is of two I kinds : (!) !hat done for purposes of plotting, and (it) that done for determining area> and volumes. The surveyor may also be called upon to do some design work specially in the case of route surveying. 1 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net I' I 24 SURVEYING 3. CARE AND ADJUSTMENTS OF INSTRUMENTS The practice of surveying requires experience in handling the equipment used in field and office work, a familiarity with the care and adjustment of the surveying instruments. and an understanding of their limitations. Many surveying insttuments such as level, theodolite, compass etc. are very delicate and must be -handled with great care since there are ml11ly pans o f an instrument which if once impaired cannot be restored 10 their original efficiency. Before an insnumem is taken out of the box. relative position of various parts should wbe carefully noted so that the instrument can be replaced in the box without undue strain on any of the parts. The beginner is advised to make a rough sketch showing the position wof the insttument in the box. Following precautions must be taken : I . While taking out the instrument from the box, do not lift it by the telescope wor with hands under the horizontal circle plate. It should be lifted by placing the hands under the levelling base or the foot plate. 2. While carrying an instrument ftom one place to the other, it should be carried .Eon the shoulder, sening all clamps tightly to prevent needless wear. yet loose enough so that if the parts are bumped they will yield. If the head room available is less. such aas carrying it through doors etc.. it should be carried in the arms. If the distance is long, it is better to put it in box and then carried. s3. When the telescope is not in use, keep the cap over the lens. Do not rub lenses ywith silk or muslin. Avoid rubbing them altogether ; use a brush for removing dust. E4. Do not set an instrument on smooth floor without proper precautions. Otherwise nthe tripod legs are lilcely to open out and.· to let the instrument fall. If the instrument has been set up on a pavement or other sn;ooth surface, the tripod legs should be inserted in the joints or cracks. The tripod legs should be spread well apart. 5. Keep the hands off the vertical circle and other exposed graduations to avoid ramishing. Do not expose au insaument needlessly to dust, or to dampness, or to the bright rays of the sun. A Water proof cover should be used to protect it. 6. To protect an instrument from the effects of salt water, when used near tile sea coast, a fine film of watch oil rubbed over the exposed parts will often prevent the appearance of oxide. To remove such oxide-spots as well as pm:sible, apply some watch-oil and allow n to remain tor a tew hours, then rub dry with a soft piece of linen. To preserve the outer appearance of an instrtunent, never use anything for dusting except a fine camel's hair brush. To remove water and dust spots, first use the camel's hair brush. and then rub-off with fine watch oil and wipe dry : to let the oil remain would tend to accumulate dust on the instrument. 7. Do not leave the insrrument unguarded when set on a road. street. foot-path or in pasture. or in high wind. 8. De not force any screw or any part to move against strain. I f they do not turn easily, the parts should be cleaned and lubricated. 9. The steel tape should be wiped clean and dry after using with the help of a dry cloth and then with a slightly oily one. Do not allow automobiles or other vehicles to run over a tape. Do not pull on a tape when there is kink in it, or jerk it unnecessarily. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net l.j FUNDAMENTAL DEFINITIONS AND CONCEPI'S 10. In the case of a compass, do not let the compass needle swing needlessly. When not in use, it should be lifted off the pivot. Take every precaution to guard the point and to keep it straight and sharp.· I PROBLEMS I I. Explain the following terms {l) Representative fraction. (i1) Scale of plan. (iii) Graphical scale. 2. Give the designation and representative fraction of the following scales (i) A line 135 meues long represented by 22.5 em on plan. (i1) A plan 400 sq. metres in area represented by 4 sq. em on plan. 3. Explain, with neat sketch, the construction of a plain scale. Construct a plain scale l em = 6 m and show 26 metres on it. 1 4. Explain, with neat sketch. the construction of a diagonal scale. Construct a diagonal scale I em = 5 m and show 18.70 metres on it. I 5. Discuss in brief the principles of surveying. !! 6. Differentiate clearly between plane and geodetic surveying. --~ 7. What is a vernier ? Explain the principle on which it is based. 8. Differentiate between : n (a) Direct vernier and Retrograde vernier. (b) Double vernier and Extended vernier. lg 9. The circle of a theOdolite is graduated to read to 10 minutes. Design a suitable vernier i£ to read to 10\" . n10. A limb of an instrument is divided to 15 minutes. Design a suitable vernier to read to 20 'ieCOnds. e11. Explain the principles used in the cowtruction of vernier. l eConstruct l! vemier to read to 30 seconds ro be used with a scale graduated to 20 minutes. r12. The arc of a sextant is divided to 10 minutes. If 119 of these divisions are taken for :) ithe length of the vernier, into bow many divisions must the vernier be divided in order to read nto (a) 5 seconds. and (b) 10 seconds ? ,I g13. Show how to consuuct the following verniers (I) To read to 10\" on a limb divi~ to 10 minutes. ~_1 .n'll (i1) To read to 20\" on a limb divided to 15 minutes j e14. (a) Explain the function of a vernier. t(b) Consr:ruct a vernier reading 114.25 rom on a main scale divided to 2.5 nun. B (c) A theodolite is fitted with a vernier in which 30 vernier divisions are equal to w· 30' on main scale divided to 30 minutes. Is the vernier direct or retrograde. and what is its least count ? Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING 26 ANSWERS 2. (1) 6 m [ o l c m ; ~; (il) 10 m to 1 em ; \"Wk 9. n=60 10 n:::4S11. (direct vernier) (b) 11 = 60 (exlended vernier) 12 1 minute. (i~ 11=45 n=4013. (a) 11 = 120 (i) 11=60www.EasyEn14. (c) Direct ; -'f ~- 1 '' il ~­ ¥1 ... i! Downloaded From : www.EasyEngineering.net

mDownloaded From : www.EasyEngineering.net Accuracy and Errors 2.J.. GENERAL distinguish between accuracy and and , , In dealing with measurements. it is important to the instruments, the methods precision. Precision is the degree o f in perfection used the observations. Accuracy is the degree of perfection obtained. Accuracy depends on (1) Precise instruments, (2) Precise methods and (3) Good planning. The use o f precise instruments simplify the work, save time and provide economy. The use o f precise methods eliminate or try to reduce the effect o f all types o f errors. Good planning. which includes proper choice and arrangements of survey control and the proper choice o f instruments and methods for each operation, saves time and reduces the possibility n-f,·.· gineeri--~'~.-of errors. n; .. g; _: 1 .. netl; The difference between a measurement and the true value of the quantity measured known since the true value of the is the true e\"or of the measurement. and is never of a surveyor is to secure measurements quantity is never known. However. the important function .' · which are correct within a certain limit of error prescribed by the nature and purpose of a particular survey. f the same quantity; be great if e~h of A discrepancy is the difference between two measured values o it is nor an error. A discrepancy may be small, yet the error may reveal the magnirude the two measurements contains an error that may be large. It does not of systematic errors. 2.2. SOURCES OF ERRORS Errors may arise from three sources : Instrumental. Error may arise due to imperfection or faulty adjustment o f the (1) For example, a tape may be too long adjustment. Such errors are known as instrument with which measurement is being taken. or an angle measuring instrument may be out of ' instrumental errors. want o f perfection o f human sight in For example. an error may be there (2) PersonaL Error may also arise due to Observing the circle o f a theodolite. Such errors in taking and o f touch in manipulating instruments. the level reading or reading an angle on are known as personal errors. Natural. Error may also be due to variations in narural phenomena such as (3) temperarure. humidity, gravity, wind, refraction and magnetic declination. I f they are not (27l ­ .._ .· !~'- Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING T'. 'l 28 properly observed while taking measurements, the results will be Incorrect For example, a mpe may be 20 metres at 20'C but its length will change i f the field temperature is differenr. be classified as : w(b) (c) 2.3. KINDS OF ERRORS w(a} Mistakes. Mistakes are errors which arise from inattention, inexperience, carelessness wand poor_ judgment or confusion in the mind of the observer. I f a mislake is undelected, it produces a serious effect upon the final result. Hence, every value to be recorded in the field must be checked by some independent field observation. Ordinary errors met with in all classes o f survey work may (a) Mistakes Systematic errors (Cumulative errors) Accidental errors (Compensating errors). .E{b) Systematic Errors (Cumulative Errors). A systematic error or cumulative error aA systematic error always follows some definite mathematical or physical law. and a cOrrection scan be determined and applied. Such errors are of constam character and are regarded yeffect is, therefore, cumulative. For example. if a tape is P ern shan and if it is stretched. is an error that, under the same conditions, will always be o f the same size and sign. EN times. the total error in the measurement of the length will be P.N nIf undetected, systematic errors are very serious. Therefore : (1) all surveying equipment as positive or negative according as they make the result too gr;at or too small. Their em. must be designed and used so that whenever possible systematic errors will be automatically eliminated. (2) All systematic errors that cannot be surely eliminated by this means must be evaluated and their relationship to the conditions that cause them must be determined. For example, in ordinary levelling, the levelling instrument must first be adjusted so that the line o f sight is as nearly horizontal as possible when bubble is centered. Also, the horizontal lengths for back-sight and fore-sight from each instnunent position should be kept as nearly equal as possible. In precise levelling, every day the actual error o f the instrument must be determined by careful peg test, the length o f each sight is measured by stadia and a ;.;0n·;,;;;riur, iV i.i.it lc.Suhs is applied. (c) Accidental Errors (Compensating Errors). Accidental errors or compensaJing errors : are those which remain after mistakes and systematic errors have been eliminared and are caused by a combination o f reasons beyond the ability of the observer to control. They rend sOmetimes in one direction and sometimes in the other. i.e. they are equally likely I 1 to make the apparent result too large or too small. An accidental error o f a single determination is the difference between (1) the true value of the quantity, and (2) a determination that I. iS free from mistakes and systematic errors. Accidental errors represent the limit of precision in the determination of a value. They obey rile laws o f clzance 011d therefore, must be /zandled according to the mathematical laws of probability. As srated above, accidemal errors are of a compensative nature and tend to baJance out in the final results. For example, an error of 2 em in the tape may flucruare on either side o f the amount by reason o f small variations in the pull to which it is subjected. Downloaded From : www.EasyEngineering.net 1 I

Downloaded From : www.EasyEngineering.net r .o..CCURACY AND ERRORS 29 I 2.4. THEORY OF PROBABILITY ! Investigations of observatioru of various types show that accidental errors follow a r definite law, the law o f probability. Tbis law defines the occurrence of errors and can ! be expressed in the form o f equation which is u s e d to compute the ptobable value or ~ the probable precision o f a quantity. The most imponanr features of accident!l (or compensating) 'r errors which usually occur. are : (z) Small errors tend to be more frequent than the large ones; that is. they are more probable. (ii) Positive and negative errors of the same size happen with equal frequency ; I that is they are equally probable. the (iii) Large errors occur infrequently and are improbable. ,~ Probability Curve. The theory of probability describes these featutes by saying that relative frequencies o f errors of different extents can be represented by a curve as I in Fig. 2.1 . This curve, called the curve of error or probability curve. forms the basis '' for the mathematical derivation o f theory o f errors. .•tfr' Principle o f L<ast Square. According to the principle of least square, the most probable n''l: value o f an observed quantity available from a given set of observations is the one for >'~ whicll the sum o f the squares o f errors (residuals) is a minimum. I g • P.! ~ inee v ..~ ;; Most Probable Value. The most probable value of a quantity is the one wbich has more chances of being correct than has 401 • any other. 17re most probable error is defined • as that quantity which when added to and subtracted ~ 310 from. rlre most probable value fixes the limits • ,,--;:;,-within which it is an even clzance the true value 1/ • 0~\" 2 '0 of the measured quantity must lie. I/ •• ~ 10 • The probable error of a single observation is calculated from the equation. •' r Size of error I\\ :j iThe probable error of the mean of a number 0 nof observations of the same quantity is calculated 1'\\. :.-1 '\\-... -0.6 I g..~ 0 . E..= ± 0.6745 'J :1:=1-'-;1- ... (2.1) +0.2 +0.4 0 -0.4 -0.2 1 netwhere FIG. 2.t PROBABILITY CURVE. from the equation : Em= ± 0.6745 ._; l:v 2 E, ... (2.2) n (n - I) = vrn. Es = Probable error of single observation v = Difference between any single observation and the mean of the series I.' were Em = Probable error of the mean eight readings 2.306. 2.312. n = Nwnber o f observations in the series. Example 2.1. ln carrying a line of levels across a river. tlze following taken with a level under identical conditions : 2.322, 2.346, 2.352. 2.300, 2.306, 2.326 metres. 11 I Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING 30. Calculate (I) the probable error o f single observation, (il) probable error of t!Je mean. I Solution. The computations are arranged in the tabular form : ~-~odrrading-- ' - - - - -- .,/ ---~ l~ 1' ~ I I 2.322iO.llOt I' 0.000001 I 0.025 2.346 !' 0.000625 I w2.352 0.031 I 0.000961 ' 0.015 0.000225 2.3060.009 I wI2.312 0.000081 2.3000.021 0.000441 I w2.306 .2.326 EMean : 2.321 aFrom equation (!), , . . - - - - O.oi5 0.000225 ...j ·~ ~~ s£, = ± 0.6745 0.005 yEnand 0.000025 I !:v2 = 0.002584 0 0 84 = ± 0.01295 metre E, 0.01295 ··. TnE., = = ±~ = ± 0.00458 metre. 2.5. ACCURACY IN SURVEYING : PERMISSffiLE ERROR The pemJissible error is the maximum allo'Yable limit that a measurement may vary .. from the Ulle value, or from a value previously adopted as correct. The value of lhe permissible error in any given case depends upon the scale, the purpose o f the survey. · the insuuments available. class o f work etc. The surveyor may be handicapped by rough country, roo shan a time, too small a party. poor instruments. bad wearher and many· · ot.her unfavourable conditions. The limit of error, therefore. cannot be given once for all. Examples of the permissible error for various classes o f work have been mentioned throughout J this book. However, the best surveyor is not he who is extremely accurate in all his wuJk., but lie )vhq does it just accurately enough for the purpose without waste o f time or money: A swveyor should m~e the precision of each step in the field work corresponding to the importance o f that step. Significant ,FigUres in Measurement In surveying, an indica[ion of accuracy attained is shown by number of significant ¥ figores. Each such quantity, expresse<) in n number of digits in which n - I are the digits o f definite value while the last digit .is the least accurate digit which can be estimated I and is subject to error. For example, a quantity 423.65 has five significant figures. with four certain and the last digit 5, uncertain. The error in the last digit may. in this case, be a maximum value o f 0.005 or a probable value o f ± 0.0025 1 ~ Downloaded From : www.EasyEngineering.net

ACCURACY A..\"'D ERRORS Downloaded From : www.EasyEngineer31ing.net I As a rule, the field measurements should be consistent, thus dic1ating the number of significant figores in desired or computed quantities. The accuracy o f angular and linear ~' values shoJild be compalible. For small angles, a r c = chord= R 9\" 1206265, where 9 is expressed in seconds o f arc. Thus for !\" o f arc, the subtended value is I mm ar 206.265 m while 'p. for I ' of arc, the subtended value is I mm at 3.438 m or I em at 34.38 m. In other words, the angular values _measured to I\" require dislances to be measured to 1 rom. while the angular values measured [O 1' require dis[ances to be measured to 1 em . Accumulation of Errors: In the accwnulation of errors of known sign, the summation is algebraic while the swnmation of random errors of ± values can only be compmed ~'· -J±by the root mean square v~a::,lu~e....:..:- - - - - - er = e12 ± el ± e32 ± ......·. ± ei ... (2.3) I 2:6. ERRORS IN COMPUTED RESULTS ~ The errors in .computed results arise from (1) errors in mea.iured or derived data. ;' or (il) errors in trigonometrical or logrithmcial values used. During common arithmetical - ; process (i.e. addition, sub[racrion, mulriplication, division etc), the resultant values are frequently I~ ' given false accuracies as illustrated below. (a) Addition. n s ± es = (.r ± e.t) + (y ± ey) Let s = x + y, where x and y are measured quantities. s + os = (x + &x) + (y + oy) g Probable ErrorThen where 5s may be + or - . i~ ntt. LetConsidering probable errors of indefinite values, 1or s ± es = (x + y) ± e} + e/ e1 s + os = (x - v) + (ox + ov) ~ ... (2.4) ... (2.5) ± es = i/ e} + e / . eThe maximum error= os = (ox + oy) r~ Considering probable errors of indefinite value. s -± e s = (.r - y) ± { e} + e_v! (b) Subtraction. ' i·I S=X-y nV·~ J gwhich is the same as in addition. .(c) n¥\" Lets=x.y Probable error ±es = e} + e / eOSx=Y. ox and os,. =X. oy I tThe maximum error Multiplication os=yox+xoy Considenng probable errors o f indefinite values, e s =\"<Y/ 'e . x' + x'e y' ... (2.6 a) 1 ~. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net !\"I! 32 Sl'RVEYING ! or .e, = xy Y(e , ! x ) ' + (e y l y ) ' \" . ( 2 . 6 b) and error ratiowLet '!s!. = ..fce,lx)' + (eyly)' .... (2.6) (d) Division ... (2.7 a) wThe \".(2. 7 b) S =X- \" . ( 2 . 7) y wConsidering probable errors of indefinite Bx and Bs, = x By &s.r =y- y' '!/(~)' .7JE'e, = maximum error Bs= B x + x . By .y y' asor values, yEand error ratio : +( e1 = x- ~(e2\\)+2 1 . .(.e! .) ' \\y yX nwhich is the same as for multiplication. ~ = ..f(e,f x)' + (ey/y)' s (e) Powers. Let s =X' Bs = n x\"-'Bx . . Error ratio Bs nBx ... (2.8) SX Example 2.2. A quanJity s is equal to the sum of two measured quantities x and y given by s = 'l.dd + 5.037 Find the most probable error, the maximum limits and most probable limits of the quantity s. will Solution. errors The maximum errors (Bx and By) will be 0.005 and 0.0005 and the probable be ± 0.0025 a n d ± 0.00025. ... (!) . . s +lis= (x + y)± (Bx +By)= (4.88 + 5.637) ± (0.005 + 0.0005) = 10.517 ± 0.0055 Also = 10.5225 and 10.5115 s ±e, = (x + y) ±..J :1 + e,' = (4.88+5.637)± Y(0.0025)2+(0.00025)2 = 10.517 ± 0.00251 ... (2) = 10.5195 and 10.5145 Downloaded From : www.EasyEngineering.net

r Downloaded From : www.EasyEngineering.net ACCURACY AND ERRORS 33 (s) Hence the most probable error = ±0.00251 and most probable limits o f the quantity are 10.5195 and 10.5145. Similasly the maximum limits o f quantity ase 10.52is and 10.5115. quantity s, consisting o f the sum of two quantities 10.51, decimal place is the From the above, it is cleas that the and that the second quantity Hence it is concluded may be expressed either as 10.52 or as (s) may be quoted. figure used. exceed most probable limit to which the derived the least accurate that the accuracy o f the suin must not Example 2.3. A quantity s is given by s = 5.367- 4.88 Find the most probable error, and the most probable limits and maximum limits of the quantity. Solution. b e ± 0.0025 . The maximum errors will be 0.0005 and 0.005 and probable errors will . . s +lis= ( x - y) ±(Bx + liy) = (5.367 - 4.88) ± (0.005 + 0.0005) =0.487 ± 0.0055 =0.4925 or 0.4815 n Most probable limits of s = 0.4950 and 0.4900 and maximum limits of s = 0.4925 .and 0.4815. Also s ±e, = ( x - y) ± ..J e} + e}= (5.367 - 4.88) ± Y(0.00025)' + (0.0025)> 'Jg.i = 0.4925 ± 0.00251 = 0.4950 or 0.4900 j inof Hence the most probable error= ± 0.00251 I eas under : Here again, the quantity s can only be 0.48 or 0.49, and the second decimal place the most be given. Hence the accuracy probable limit to which a derived quamity (s) can ei Fit.Jis subtraction must not exceed the least accurate figure used. Example 2.4. A derived quantity s is given by product of two J riSolutiona measured quamities, nThe maximum errors in the individual measurements will be 0.005 the most probable errors will be ± 0.0025 a n d ± 0.0025 respectively. S = 2.86 X 8.34 r.;rror and ll!DSI probable -;~J-­ gNow max. error Joi: :r.w.in~m error in rhe derived quanrf~· .=0.0417 + 0.0143 = 0.056 ~ 0.06 ~(-~ 7)' n~e(OZ0~~t5)'+ (!!8~~~The and 0.005, while lis= y Bx + x By= (8.34 x 0.005) + (2.86 x 0.005) most probable error r'i\"-s_ __ 5 e, = X y )' + ( = (2.86 x 8.34) )' Now = ± 0.02 S ='x X y = 2.86 X 8.34 =23.85 Downloaded From : www.EasyEngineering.net

r DIownloaded From : www.EasyEngineering.net SURVEYING I 34 I Hence the most probable limits are thus 23.87 alld 23.83, alld by rounding off prOCO$S. value may be given as 23.85, i.e. to the same accuracy as the least accurate figUre used. Example 2.5 A derived quanJity s is given 1Jy s =82.33.94 Find the maximum error and most probable error in the qudHiity. Solulion wThe maximum error Ss is given by wwhere wrespectively Bs=fu:+x.By y y' (maximum errors in illdividual .8.34 EThe probable errors in individual measurements are ± 0.025 and ± 0.0025. 0.05 0.005 Bx and By measurements) are alld aprobable error in the derived uanti se,=! (~!!.)' +(~)' =~..Ji(o,02S )+(0.0025 )'. Bs = 0.05 + 23.9 x 0.005 ,. 0.006 + 0.0017 = 0.0077 yy X (8.34)2 Hence the EnNow is _ y 8.34 23.9 8.34 = ± 0.003 s = 23 ·9 = 2.8657 ~ 2.866 8.34 Hence the most probable limits of s are 2.869 and 2.863. For practical putpeses, adopting rounding off, the value may be given as 2.87. Example 2.6 A derived quantity s is given 1Jy s = (4.86) 2 Find rhe ·mtrr;mum wr!ra• o f c'·-··-;.•· -_--::-:d ;r:,_..,.s! p,-,_>Z;c.;!;; .J.I.:.;;; t' .. ,. ' ' Solution \"J ~-' . . . . . . s = (4.86)2= 23.6196 Now maximum error in the individual measurement is 0.005 and. probable error in measurement ·is 0.0025. Now, maximum error Ss is given by os = n t•-• Bx = 2(4.86)2' 1 x 0.005 = 0.0486 The most probable value of error is e, = n x\"''e, = 2(4.86)2' 1 x 0.0025 = ± 0.0243. The most probable limits of s are thus 23.6~39 and 23~5953. and rounding these off, we get s, practically·, equal to 23.62. Downloaded From : www.EasyEngineering.net