BC Punmia SURVEYING Vol 1 - By EasyEngineering.net

1.BVELLING Downloaded From : www.EasyEngineering.net 235 appear more apparent. The vertical scale is kept 10 times the horiwntal scale (i.e. I em= I m). The reduced levels o f ·the points are also writteo along with the bOriwntal distances. -·B.M. ! LEVEL FIELD NOTES FOR PROFILE LEVELLING J•.•. nJ. . .h H R,.<, F..<. H. I. R.I.. RtllUIIb 'I 2t£<M 210.455 2.1\"'' 'I 10 2.680 209.820 ij ? 10 2.860 209.640 ,,1 3 20 2.120 210.380 4 35 2.975 .:~:'l'iJ ?00.525 '~ T.P. 1 1.005 2.8\"\" 21•.645 \"\"\".640 .'l'i 5 45 2.810 207.835 ''I 6 ..•3 2.905 207.740 1 2.530 208.115 ,: ~ I 80 1.875 208.170 •• 115 1.0?< 208.720 ,,!I:J;I\" 207.650 T.P. 2 2.160 2.995 209.810 ·~ 10 125 0.825 208.985 ~:! 11 145 1.020 208.790 ~ 12 162 1.6?< . 208.185 *I 13 180 2.080 207.730 I T.P. 3 FaU 206.825 gine 8 9 ·,o 5.210 2.985 f n Checlc 210.455 8.840 Fall 206.825 ~ 5.210 3.630 '''I 3.630 '( .. eri205.001 13 II ~ ~ .. nDalwnl:l ' 0' '' .~.'. \"~'' ~' ~' :'g ~' .\"m'' g' 'Ji ..R.L S1\"0' fil ~~ ~ :.!! ~ la !il 8 ~ :::: g.net\"'DlstancesO i!l 115 125 162 !il ·,~ N N N 20 N 180 'I 145 35 45 63 80 98 II l Longitudinal Section lj Scale{ Hor. 1 <:m=10 m Ver.1cm::r1m l FIG. 9.43 iIi Levelling to Establl.sb Grade Points : This kind of levelling, often referred to as 'I' giving elevalions is used in all kinds o f engineering construction. The operation of establishing grade points is sintilar to profile levelling and follows the latter. After the profile bas l' ! I Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 236 SURVEYING bbftchoeaeererfronihreeeaedpiclgohgfhtootterisnwdtoagaftairodntihnndetboiytsihnetslhkutegrnmuromaiwfndieengenl.dtlps.iTonahieTnethdhsei.aas.smtTalenobhvcueeeenelntlgseirnqeagousdtafealobcppltuioeostrihanteothtdieroinsofgnirelsalsttdtaha£arebttslripseohrafdorceofhdimrleebapydomtihinnamegtp,e,abausrethuesneircnihtnghggurm!ashddaeoedrwkefentoelleralmvonawfdirtnoiioenmidnsg wA grade stake is driven in the ground and grade and read wi!h the help o f level. The stake is driven in or wis the saine as calculated abOve. Before proceeding the work prepared giving !he rod. readings at each point to set it Grade point elevlllion 'C H.L.- Grade rod reading. w9.18relation. rod is kept on the top o f it oUJ till !he grade rod reading .readings .were obtained : in the field, a table is generally on a given gradient. Example EB.S. aFrom the sbe ser ow on y181.580. Work makes !he procedure clear. 183.215, the following Example 9.18. In running fly levels from a bench mark o f R.L. 1.215 2.035 1.980 2.625 0.980 Enifo=sofr1tt8ahw5ke.eh2Sni0fcoi5hrlosut-ntcipoa1esnn8gt.a1bt.i5iIseon8n0tdo!o=Nhnebo3ee..6fia21r4ss58,t1u.!ps5h.ua8era0Ttl.h.heoeHiFfgeohrntrehtcaeed!ohifqneGugcrelaoasdlitsslieiotmnsrea,oenttdittofeilnrnyregedacldoeoivimfnnegelthlsi!=enhgoeiunHtwIs..ta!Str.sou. m-dbceoeonGoltue,r1,ma8dw5ntehh..2eep0nTo5cih.onaemtTbpehRalueec.tLvkaRats.iitog.iLonohns.tfF.S.0.965.3.830 intervals are to last position of the instrument, five peg~ ·'i!t 20 metres have a R.L. of a uniform rising gradient of I in 40 ; the 'jirst peg is to the pegs the ori oUJ the staff readings required for setting rhe raps of given gradient. l*the next peg at the rising gradient of 1 in 40 will be 181.580 + 1 x = 182.080 and its grade rod reading will be 185.205- 182.080 = 3.125. Similarly, !he rod readings for o!her pegs are calculated as entered in !he table given below : I. Dist. l.S. F.S. H. I. R.L RellllUts S. No [--·B.S. 0.965 184.340 183.125 -------~-~--~-~ 3.625 3.830 !85.410 183.375 ' 3.125 0.980 183.560 181.580 Ij 1.2!5 2.625 !85.205 182.580 2.125 !.625 181.580 2 2.035 7.400 Rise 182.080 182.580 3 1.980 183.080 183.580 4 2.625 183.580 50 !83.125 Peg 1 0.455 Peg 2 6 ! 20 Peg 3 Peg 4 !7 40 Peg 5 8 ; 60 !: 9 80 Check 7.855 I Rise Oleckcd 7.400 I 0.455 Downloaded From : www.EasyEngineering.net

.,.Downloaded From : www.EasyEngineering.net LEVELUNG 237 9.15. CROSS-SECTIONING profile and on either side ;; They provide me data for Cross-sections are run at right angles to !he longitudinal cross-sections are numbered Jl are set out at right angles \"'' ; I o f it for the piirpose o f lateral outline o f the ground surface. estimating quantities o f earth work and for other purposes. The · ' \": :H consecutively from !he commencement of !he centre line and j,~ to !he main line o f section wi!h tb,e chain i i1 and tape, the cross-staff or the -optical ,.t: 1 i ! ( ( ,/square and the distances are measured ~i\"\\· ( 'ilI left and right fr~m the centre peg (Fig. Ai Central una 1 [,, ,/ 9.44). Cross-section may be taken at each !_·I chain. The length of cross-section depends i ~!1 :!i -@:ii _,. / • upon the narure of work. O.!I ~! O.!I c,;-~! -' c. / ! ~! The longt\"tudinal and cross-sections O.!I ! ;(J;• a?!I ! {Qj ~~j~ 'i may be worked· together or separately. ! . O! In the former case, two additioual columns c,:; fO.i ! !\"-t are required in the level field book to ! ~? o /\".J\"I ! ~ ~~ I \"-/c ~ · ~m,.•j~t.l, i \".J\".' I (J\"/ I /' ~ give the distances, left and right of the centre line, as illustrated in table below. !11 ng IStatWn AG. 9.44 inB.M. :;; 0 ~'\"I'' eL1 lo ' eLz rLl iRl n IRz R, gI .L1 nLz LJ etR1 To avoid confusion, !he bookings o f each and clearly and full information as to !he number left or right o f the centre line, wi!h any o!her cross-section should be entered separately o f !he the . cross-section, whether on the matter which may be useful, should be recorded. Dimulee (m) B.S. I.S. F.S. H. I. R.I.. Rtmorb 1.325 10L.325 L cR 1.865 100.000 Cross- !.905 99.460 section ·O 2.120 99.420 atOm 3 2.825 99.205 chainage 6 1.105 98.500 1.520 99.620 Cmss- 3 .1.955 99.805 section 7.5 1.265 99.370 1.365 101).060 at 10 0.725 99.960 20m 20 2.125 !00.600 chainage 3 1.925 99.200 6 99.400 9 3 112 7 2.250 99.075 100.435 /!] 10 0.890 I T.P. 2.120 99.205 O>ecl< !.325 2.120 100.000 1.325 99.205 - - -. . .L..... Fall_ 0,]95 Fall 0.795 Downloaded From : www.EasyEngineering.net

7 Downloaded From : www.EasyEngineering.net SURVEYING 238 Plotting the Cross-sec- ~ L, R, tion (Fig. 9.45) L, R, R, Cross-sections are plot- Datum 95.000 ' ,• ted almost in the same manner mCo·~' I Dc8o.0 . -qmmo~. ~oq0..- mo~Ol. Ill~ as the longitudinal sections ex- 9 6 3 0m 3 !:;:~ cept that in this case both the m. o0 scales are kept equal. The point 0)..- walong the longitudinal section 7 10 is plotted at the centre o f the horizontal ·axis. The points to wthe left of centre point are prOt- red to the left ·and those to wthe right are plotted to the right. The points so obtained are .joine<;l. by straight lines. E·' .. a9.16. LEVELLING PROBLEMS The following are some of the difficulties COI1IIDO~y encountered in levelling s(!) Levelling on Steep Slope. See § 9.11 Cross-section at chalnage 20 m Scale1f HVeorr.. 1 em= 1m 1 em= 1·m FIG. 9.45 y(2) Levelling on Snmmits end Hollows. Ecan In levelling over summit, level be sighted without extra setting nlevel should be set only sufficiently should be set up sufficiently high so that the summit (Fig. 9.46). Similarly, in levelling across a hollow, low to enable the levels of all the required points to be observed (Fig. 9.47). Levelling over summit Levelling across hollow FIG. 9.46. FIG. 9.47. (3) Taking Level of en Overhead Point T IB.M. When the point under observation is higher than the line of sight, staff should be kept invetted on the overhead point keeping X the foot of the staff touching the point, and ~ :~~: =~gh:h~~:a~ ~~~b:e:;e ~ ~! '\"''Lreading should be taken. Such reading will I~ J ; - r m m n n m m m m n m ; m ; ; m ; n ; ; n ; ; ; n no?r. get the R.L. of the point (Fig. 9.48). On FIG. 9.48. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEn2g3i9neering.net LEVELLING oto9hn.ne5).llchhoeeS(n4otp)rdaoetrihsynca,tLrtiepsivttfhiehool~nsuliuelndcgphmabgaPepeyooinsntbudhtebsattthaneaetonphrpededeonpsLspftraaookftromfteusnhbiattehtsyoeotbefroemeWredpnuoimdcrheaeisdreytladtokleebv,ienbenlveictehntSoiesimdgg.hawerttekedl,lthteaAhlescoHrob.s!at.sock(s(mSFigeaihgekt.e erx9aea.a4mdn9ipo)nltgee !apbokkateeenfkgeoeopwldnnhiranneeing.WovdefepnhTntehetdhrhgneeeet,aoodtsfiihftntnhataeshtcgefhtetfreupRttomaoohp.nkntaLeohdetnn.esnttrd.thh,oeaiessTfnikddhtestoieeheun.pplersafnitRaknrLouceg.eLemsfsve>.ieet.ttoalnhsfrooteemnftsoatsaptixteoyolhilcolsefohlwbneuwierdtssaohitpdesfpkireiwdrenosegoiitftts.whonsnatAehetbhatedelreaedntvipotdsnweheiglgegaohtthsenrtbuereaheadrnefndsalskuecaisrvdecotfee.aarafolnfclfsideAtnwsh.,grearepAetaeaeaodsrdgdtpivsanieniafsgmmrfgnuataritalfiyktaoaigoesrcnepbesttpethameekciogsdaaenyrnnRimtvht.eabbLhbuYyneees. carried further. n (5) gIf Levelling across ponds ito na FIG. 9.49 Levelling Across River river is less, the method of reciprocal levelling is to be used. If the widlh of theeering.netolfogtomtimhoosofiffepvopoaterdlsstehheooiRiggeteffto.nhThh(tILouh6ntettwtn).hcawhshneoeeiiatisHntohtlnhlwtfectwge.ehLllatar.oeeaassetlshsltlnweevhlesecds.letceeaiethslolsrKnlelSmtin.rtognmnueodtapttgoachophhTyehdwaetahhcinosPnnoaeaaeufringfrasfrenraiedtsaevsgcht,tleddsheemehi.i.rredenetwfalieohgfaTIylchiewnedsfaghentiloawhaenngbltlffHhgthlehhfh.eR,eete.WthIhn!i.tT.Lgeaaaeo,wfakhkhi.fsrlaeteelsushwtlnonuthlbeto..hafeiititgfcrlnealoaSlahTsbhcnltsUttelhehrarseeeuvcetne,aodhtmetdhfomflwftvleepo,irfeannaerhptrorhgtaoeitktnmedihnfscovmiieanonfietwtshlagptrthihyets,tealeehdaetmlrdaleraiwwtsfhathRftiadheaaowmsele.ibentlnnLgcaanaocahlf.rivelansfktbcetaeoaditbowsnhfbtadtehfuthesietetmlshwedhbhllhieeehekfhketaleeteinei«ostnnptciso!uowgetacwrphtroatehtfhrntildolooe,inlle.oeoifvmdftawfTtHemrhbcarohthet.otohtfmaeleoeiove.lordrulerkoeinicwmwntwthhhwsattaaiileahhternlentrillrdeietvguldoh.emmngsllwliiitielanvdihhnitnrilieeeseeekslst be sighred across, levelling may be contintted from one side lhe river is too wide to shown in (4) with lhe other in the manner little error, provided care is taken to choose comparatively still stretch and to see that water levels are !aken at points directly opposite each olher. and the height of the instrument is then calculared. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 240 SURVEYING 9.17. ERRORS IN LEVELLING All levelling measurements are subject to three principal sources o f errors w(l) lnstnunental (a) Error due to imperfect adjustment. (b) (c) Error due to sluggish bubble. (d) Error due to movement o f objective (e) Rod not o f standard length. Error due to defective joint. ww(2) Natural slide. (a) Earth's curvature. (b)· Alliiosphe'ric refraction. (c) Variations i,n temperature. (d) Settlement . o f tripod or turning .(3) Personal points. E· a(d) Errors in sighting. (e) Mistakes in recording. (e) Wind vibrations. sINSTRUMENTAL ERRORS (a) Mistakes in manipluation. (b) Mistake in rod handling. (c) Mistake in reading the rod. yEnbbobbloeeeefn· gtiihecennleuriccmmT(loaibhnroiu)nrueerleabadc.Etbtetsie.lvsrhduesreopeTo,rwtnburthteyapbeirareaddl.rbeusttiharaecIrladofuaonjnlrrtuatochsridatelinmynloIlgwimentninfhspnttohwteerreuoeragfrsmrfoeoidbgiecdsaanhntcgttkwslre.Aesihvuasidugeepdnhnljniuntloesogitsstthrasmeniwtneddhcinaoblalt~twurf.beontbabrheedlei.essjaipgulriihstssnoatttepekmcoeedeepornintnsfitttohrat,nseoniiadlgcllt,ehhrsatuet.nwonsdlhhTitaneahhtDreheeeezobideagferirlzsolrsatdopaiggbrnaharcraceteliilskanlw.deseailili.nngilkdlghtoesteslyitawchaxaertiisonlerl f(b) Error due to Sluggish Bubble v cmoobansyestravcnIirntfegesptohtuehbrecabecubkbuobbftlobealercmisoaorrfystelaeucnrtgcgetpihsoehasn,idttiaoitrndgeewltwaiylhlb.ialecsHoomtbhweeeeenvtseoirgs,hirgetthhstteiesdi.enbrerToiwnhrgreomntgeaarykreponobr.seiitSsipouancrc,htoiamelalvpyeebnnausvabttohbiinoldegue.gdihs it a ~- by f -~; (c) Error In the movement ·or the Objeetive SUde i f the objective slide is slightly worn In the case o f external focusing instruments, In the short sights, the objective slide our, it may. not move in truly horizontal direction. is, therefore, more. Due to this reason, is moved out nearly its entire length and the error is compensating and can be eliminated extremely short sights are to be avoided. The error by balimcing backsight and foresight, since in that case, focus is not changed and hence, the slide is not ·moved. (d) Rod not of Standard Length rod cause errors similar to those resulting from is systematic and is directly proportional to the · Incorrect lengths o f divisions on a a measured difference incorrect marking on a rape. The error Uniform wearing of difference in elevation. I f the rod is too long, the correction is added to in elevation ; if the rod is too short, the correction is subtracted. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net'jj 241 :.i,l LEVELLING :~ j the shoe ··ar the bQnom o f the rod makes H.!. values incorrect, but the effect is cancelled 1'1: wben included in both back and foresight readings. For accurate levelling, the rod graduation ;;~'' should be tested and compared with any srandsrd tape. (e) Error t o Defeetive Joint i·• du' e the rod down 'on :'!! The joint o f the extendable rods may be worn out from sening interval may result test the rod at frequent ' '1n.j the run' and from other sources. The failure to in ~ large cumulative error. ~::~ ~-·. ., 1 NATURAL ERRORS ~: \\ (a) Earth's Curvature is to increase the rod readings. Wben the distances are small for greater distances when the back and foresights are not u The effect o f curvature the error is negligible, but o f considerable magnitude is produced. 0 balanced, a systematic error ~~ (b) Refraction v ierIttetncstfriciarrsoe~cnlftpriycDoaaacnurtvhtteiiietcooyunfteolttafeoftrneewlrynceactdfrhrudoaasntfcnoctgtrieheoebnefsnera,aeircnacsttroplhtowmhiednhplsyeeeurnanvryfsaeaanntchtdoieent,hfggotlhriluneiouggeavshhteltydortehfbceaienrsenbiladgaossshcnhiktngo.gdsnpiopgatwhhesdsertniieswoatssadntanadrccfdolfeofsf,orsereteaiiintsdmtiiogniesthghttsebhi.mudeStifpsoitgonmrarmscnosaeciuybentlsohdebef.aertacoeEtucmrurbervomaoleislrmaupsnlhiawcnedteairiuvdtithceee. :.! n- f gineerin;. !,',I on a full day's run. ;l ohetptlaibhhetrefrpyserevoaepoetmdleirlsflunola.ihuicqgrlinT(icneulecgbHhidl)aitdrdoe.pne,ricardnoVoetItegwdotnncafhtsiafrhwesfeetvieehrepqacaexoertvtubpmeciweeuoacaoosinobnninnnscfvrbddsseeknatlerei.reqnuapiliavaunmenTrrwtaeevdihTeronveliientelntelaehlbltvmstmieuiwaenomfbdUgiprannbjog,aoireu·nlpcmrversgiotci•itenentmuutmtgunortoehtatirdpofseneteaeewmtsnorhsqaardprouosautrdeuifdryriigrdtftrisseseahtleihmanscti!teo.etmnoyrphfegroeaiIto.nspifytosohsrrhitneToenberec.nuahxlaiedmesectstThuejieaeohednetebcnhne.dneeta,daenatThdtntitbhsiejhdnoeueuaetgrftsttoreiueaonmeitrnnehtrgrrhedsfpeorefnomoreoatsrrcfvaatfaretpyiooraaidptismrflhlirisypeseouirticshnobscdpileuagdejhirewbsavusactllcencfiualtenrtlyesgrriosmcbemtveaearmaeiruldnaclordamylcotfkhibaredemewsypenelpelitonillnurtwnelrtheaegnvitecisilcteleu,ihlaqlatalhnuubribtabnosoeoalueneegddtlft gunder cenain conditions it may become systematic. fl'i·i· .netpfbbsoeoealttciltwnolketwsesieig(Iwnntofhfg)irtllltahfwtSokhebieireelnetlttgsrltiibuetgpomerahoontdei,tufnogogtotshrreeeeptoagstolitfroeg.iesbnhaTsttSteirisnriamavepnnteiodttdldlhadeersHltf,yhoo.i,eIrnnt.ehtseiefifcrTogvalehulalaroctlrruwnowtlitiuranhnitrlaggenilstdinbbePagewlaloawcitpilkpolans.oyosetibissgneshtmsbtytesaosietlntowlettmleaegtenashrntdeeiacit·lnt.ahnakeenTitxnhdhtegeulet.sshvae,ienat ttwiberoureahnvpscea,uktlolhstietfighntrhhetgharthetoeealbtneeuslvdtearranriptpvisituhooeegednds )j :\\. : '!·~I :,,,,, ·'Li! I'·ii .~::\\j! I ',~•, il ~! ; will always ·b<; too high. •I I• Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net Sl/RVEYING 242 (e) Wind Vibrations High wind shakes !he instnunem and thus disrurbs the bubble and !he rod. Precise levelling -work should never be done in high wind. (a) Mistakes in Manipulation These include mistakes in setting up the level, imperfect focusing o f eye-piece ·and of objective, errors in cemring lbe bubble and failure to watch it after each sight, and errors due to restiog the bands on ttipods or telescope. In lbe long sights, !he error due wto the bubble not being' centted,at the time of sighting are more important. Habit should be developed of cbecldDg the bubble before and after each sight. Parallax caused by improper wfocusing result in incorrect rod r~~s_,;jit produces an accidental error and can be eliminatcyd PERSONAL ERRORS w(b) Rod HandUng If lbe rod is not in .directly with the magnitude of the rod rea<!ing and directly as •he square of the inclination. EIn running a line of levels uphill, backsight readings are likely to be increased more than by carefully · focusing. aSimilarly, the elevation of a bench mark at fue· lxittom, while levelling downhill, will. be • will be too great. The error v~es the reading stoo small. Thus, a positive systematic error results. Over level ground, the resultant errorplumb,taken yis accidental since Ea special attacbmem devised for plumbing lbe ro<i' or by waving the level rod slowly towards foresight from this source and the evelvation of a bench ilclik on top will be too grOat. nor away from the level thereby taking the minimum rod reading. Vertical cross-hair may ~ the backsights are about equal to lbe foresights. The error can be minimised by carefully plumbing the rod ~ither by eye estimation or by using ·a rod level, be used to plumb lbe rod in the direction ttansverse to the line o f sight. (c) Errors in Sighting The error is caused when· it is difficult to tell when lbe crossbair coincides with !he centre of the target in a target rod and to determine !he exact reading which the cross-hair appears to cover in the case of self-reading rod. This is an accideutal error the magnitude of which depends upon the coarseness of the cross-hair, the type of rod, We: form of wget, atmospheric conditions, length of sigh[ and tile observer. (d) Mistakes in Reading the Rod The common mistakes in reading the rod are : (I) Reading upwards, instead of downwards. (iz) Reading downwards, instead of upwards when the staff is inverted. one (iiz) near !he level and only Reading wrong metre mark when lbe staff· is metre mark is visible through the telescope. (iv) To omit a zero or even two zeros from a reading. For example, 1.28 instead of 1.028 or 1.06 instead of 1.006. (v) Reading against a stadia hair. (Vi) Concentrating more attention on decimal part of lbe reading and noting whole metre reading wrongly. Downloaded From : www.EasyEngineering.net

LEVEUlNG Downloaded From : www.EasyEZn4gj ineering.netI,II ill (e) ~es in Recording and Computing '\" The common mistakes . are : of 1.422. (z) Enterin$ the reading with digits interchanged i.e., 1.242 instead man. (iz) . Entering· backsights and foresights in a wrong column. . (iii) Mistaking the numerical value of reading called out by the level (iv) Omitting the entry. ... · (v) Entering wrong remark' against a reading. backsight (vz) Adding a foresight instead of subtractiog it and/or subtractiog a reading instead o f adding it. (viz) Ordinary arithmetical mistakes. Uno of sight ''li --------------------- Example 9.19. Find the error o f reading of a ' level staff if the observed reading is 3.845 m at the i!) point sighted, the .staff being 15 em off lire venicol .:i through the borrom. ·; Solution. ~ ·;.1 In Fig. 9.50, let AB be the oliserved staff reading ': and let AC be the correct staff reading. . AC= ~ A B ' - Be' ;!,(, Evidently, = ~(3.845)1 - (O.I5f .I = 3.841. ,!;,, 9.18. DEGREE OF PRECISION FIG. 9.SO. ] n The degree of precision depends upon (z) lbe type of instnunent, (il) skill of observer, g(iii) character of country, and (iv) atmospheric conditions. For a given instnunent and atmospheric ' conditions, the precision depends upon lbe number of set-ups and also upon the length inof sights. Thus, the precision on plains will be more than that on bills. No hard and fast rules can be laid down by means of which a desired precision can be maintained. eeHowever, rwhere iE' = permissible closing n.. ..... be expressed as the pennissible closing error can E' =C ' -JK (in English metric units) E =C -JM or (in g I~pe of sumy on4 PUIJJO\" units) E =permissible closing error in feet; C =constant ; M = distance in miles .(1) Rough levelling fur reconnaissance or preliminary K = distance in km. nsurveys. : e '(2) Ordin.ary levelling for location and construction error in mm; C ' = constant the differCftl value.s, ·. . . . . . . . . . . . . . . .CI - -tb-l-e .2. ,i-ve- s- Error in feet (EJ Error in mm (E') ± 100 -{/( ± 24-{/( tsurveys. ±or& I ±0.1-& (3) Accurate f~elling for principal bench marks ±0.05-& ± 12.0-{/( or for extensive surveys. {4) Prtdse .levelJing for bench marks of widely ±0.017-& ± 4 -{/( i distributed points. ,!1 :i Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 244 SURVEYING 9.19. THE LEVEL TUBE The level rube or bubble rube gives the direction o f horizontal plane becanse the surface o f a still liquid at all points is at right angles to the direction o f gravity, and the liquid alone will, therefore, provide a level surface. For ordinary surveys the radius o f the earth is so large that a level surface is considered to be the same thing as a wThe spirit level or bubble rube consist of a glass rube partially filled with a liquid, the inner surface o f which is carefully ground so that a longirudinal section o f it by a vertical plane through the axis o f t)le wrube is part of circular arc. The rube horizontal plane. is graduated on its upper surface and wis enclosed for safety in a metal casmg. At the ends of the casing are capstan .headed screws for securing it to the Erelescope or any other part (Fig. 9.51). Before it is sealed, the rube ais partially filled with a liquid of low sviscosity, such as alcohol, chloroform or sulphuric. ether, leaving a small space which forms ya bubble of mixed air and vapour. Spiriruous liquids are used becanse they are less viscous, .i.e.. flow more freely than water. Also, these liquids have a relatively low freezing point Ebut a greater expansion than water. To minimize the effect of expansion, the proportion nof liquid and vapour must be carefully .regulated: Under the action of gravity, the bubble FIG. 9.51. BUBBLE TUBE. will always rise to the highest point o f the rube, and thus comes to rest so that a tangent plane to the inner surface o f the rube at the highest point o f the bubble defines a horizontal plane. The sensitiveness of a level rube is defined as the angular value o f one division marked on the rube. It is the amount' the horizontal axis has to be tilted to cause the bubble to move from one. graduation to another. For example, i f the tilting is 20\" of arc when the bubble moves 2 mm (one division), the sensitiveness o f the level rube is expressed as 20\" per 2 mm. A tube is said to be more sensitive if the bubble moves by more divisions for a given change in the angle. The sensitiveness o f a bubble tube ~ be increased by : (i) increasing the internal radius o f the tube, (il) increasing the diameter o f the rube, (ii1) increasing the length o f the bubble, (iv) decr~ing the roughness o f the walls, and (v) decreasing the viscosity o f the liquid. The sensitiveness o f a bubble rube should never be greater than is compatible with accuracy achieved with the remainder o f the accessories. 9.20. SENSITIVENESS O F BUBBLE TUBE the angular value o f one division division is kept as 2 mm. There The sensitiveness o f the bubble rube is defined as · o f . the bubble rube. Generally, the linear value o f one ..JIIl'. two methods o f determining the sensitivity. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net LBVELLlNG 245 First Method (Fig. 9.52) E (!)Set the instrument at 0 and level it accurately. (2) Sight aistsff kept at C, distant D from 0. Let the reading be CF. (3) Using a foot screw, deviate the bubble over n number o f divisions and .. again sight the staff. Let the reading be CE. (4) Find the difference between the two staff readings. Thus, s=CE-CF From /JJJEF (approximately), we have s .•• (1) 0 tana~:~~a.=D a. = A : = ~ FIG. 9.52. Sintil.arly, from 1'. A OB, ...(il) wbere R = radius o f curvature o f the bubble rube I = length o f one division on. the bubble rube (usually 2 mm or 0.1 in.) n..- ginrube. Equating (i) and (i1), we get Equation (1) s nl or R =nlsD- ...(!) ;I I t is to be bubble v=li an expression for the radius o f curvature o f the I ... (2) above gives D and s are expressed in the same units. i noted that ~ eering -JBut ! Again, from .(il) we have a. = ~ ., . . a ' = sensitivity o f the bubble tube = angular valne o f one division is given by ;~ a'=~ by putting n = 1 ... (3) ' R =n i D- (from 1) • s .nor a ' = _ I _ = ..!..._ radians = ..!..._ x 206265 seconds . . . (4) niD nD nD 1 -sin 1\" s etEquations (3), (4) and (5) give the expression for the sensitivity of the bubble tube. (Since I radian= 206265 seconds = a • = nD s seconds . . . (5) sin 1\" Second Method (Fig. 9.53) ( ! ) Set the instrument at 0 and keep a staff at C. (2) Move the bubble to .the extreme left division. Read both ends o f the bubble. Let the reading on the left end o f the bubble be 1, and on the right be r,. Let the staff reading be CE. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING \"'· · · ? : 246 (3) Move the bubble to the extreme right division. Read both ends o f the bubble: Let the reading on the left end o f the bubble 11 be and on the right end be r1 • Let the staff reading be CF. (4) Find the difference between the two w(5) Let A and B represent .the centres wof staff readings s = C E - CF w(11 - r,) -: (1,- r,) divisions( the bubble in the two positions The net travel of the bubble wiU'~ei;lua! .Consider the .left divisions as positive. and right divisions as negative. beEnumber of divisions through which the bubble has been moved. Then a(1, - r,) - (1, - r,) FIG. 9.53 n2Let n = tot31 s(6) Considering similar triangles GEF and ABO, we get. as before, ... ( ! ) yR= n/D ... (2) ·~ Es na =s- =n-l DR a ' =I- rad\"tans seconds . . . (3) . . . (4) .R = nsD x 206265 - - ssin · ·· seconds . . . (5) The sensitivity o f a bubble tube depends mainly on the radius o f curvature o f the tube (the larger the radius, the greater the sensitiveness): However, sensitiveness also depends upon (!) the diameter o f the tube (the larger the diameter, the greater the sensitivity), (i!) length o f the vapour bubble, (iii) viscosity and surface tension o f the liquid (the lesser the viScosity and surface tension, the greater the sensitivity). A very. smooth internal surface also increases sensitivity. Example 9.20. The reading taken on a staff I(}() m from the instrument with the bubble central was I. 872 m. The bubble is then moved 5 divisions out o f the centre. and the staff reading is observed to be I.906 m. Find the .angular value of one division o f the bubble, and the radius of curvaJure o f the bubble tube. The length o f one division . o f the bubble is 2 mm. Solution. Staff intercept for 5-division deviation o f the bubble = 1.906 - 1.872 = 0.034 m. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEn24g7ineering.ne,,t~~.1 LEVELUNG (1) The radius o f curvature (R) is given by ,;;i. R =nisD- II: Here n = 5, I = 2 mm = loO2 O m ; D = 100 m, s = 0.034 m :~ R 5 x 2xx l 0_ 0 metres = 29.41 m. ~~~t ,·1' 1000 0 034 ~~ (i!) The sensitivity o f the bubble tube (a') is given by ~~ a' = nsD x 206265 seconds = s.0;.103o40 x 206265 = 14.03 seconds. II one Example. 9.21. Find the radius o f curvaJure of the bubble tube if the length o f division is 2 mm and ~I~ if the angular value o f one division is (a) 20 seconds, (b) 1~ lj: 1' I miiiJlle. Solution. .1J.1·.!.' '! a' =.!. radians =.!. x 206265 seconds 4:~ R R ,,~~ wbere a' =angular value o f one division and I = length o f one division ~: 2 a' = 20 seconds ; I = 2 mm = -100-0 m 1\\~11\"',. ng R= (a) I~.L - wR = I x 206265 = 2 206265 = 20.62 m. ~ a' 1000 x 1.:·,11 iExample 9.22. If the bubble tube of a level has a sensitiveness of 35\" per 2 ~':···.'.1 a ' = 6 0 seconds ; 1 = 2 m m =10-00- m ndivision, find the error in staff reading on a vertical staff aJ a distance of IOO m(b) !il eby the bubble bending I.~ divisions out of centre.aI'x 206265=2x ~206265= 6.87 m. ' 1000 eSolotion. riWith previous 2 mm caused ng.nwhere notations, we have a ' = nsD x 206265 seconds eD =distance of the staff = 100 m tSubstituting the values in the above equation, we get a' =angular value o f one division = 35\" s = staff intercept = error in staff reading due to deviation of the bubble n =number o f divisions through which bubble is out = 1.5 = ~ = 35 X 1.5 X !00 m = O02S m. s 206265 206265 · Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 248 SURVEYING Example 9.23. Find the radius o f curvature o f the bubble tube ond the value of ends o f the bubble ond each 2 mm division from the following average reading o f the 11 o f a staff 80 m away. 1 1.602 Staff readings 1.680 10 Eye-piece end o f bubble 20 20 10 wObject glass end ofbubble wIn the first set, the. centre·. o··f·the.bubble bas moved -20--2-10 = 5 d\"tV·IS·tOns towa<ds eye-pt·ece... ... ... w~;~Ireend of the tube. In the second set, Solution. .E=•=5+5=10. The change in staff readiugs = s = 1.680 - 1.602 = O.o78 m of the bubble bas moved 20 ; 10 = 5 divisions aThe radius of curvature of the tube is given by syR -- towards objective end. The total Dllil)ber of divisions through wbich the bubble bas moved 1 Ewbere n = 10 divisionsl=2 mm= n/Dn10x2x80 ' s ~ m; D=80 m s =0.078 m R - 1000 x O.o78 20.5 m. Also, the value of 2 mm division is given by a' = -ns0 x 2.06265 seconds = -l00.0x788 x 206265 = 20.1 seconds. 9.21. BAROMETRIC LEVELLING The barometric levelling is based on the fact that the atmospheric pressure varies inversely with the height. As air is a compressible fluid, strata at low level will have a greater density than those at a higher altimde. The higher the place of observation the lesser will be the atmospheric pressure. A barometer is used for the determination of the difference in pressure between two stations and their relative altitudes can then be approximately deduced. The average readiug of the barometer at sea level is 30 inch and the barometer falls about I inch for every 900 ft of ascent above the sea level. This method of levelling is, therefore, very rough and is used only for exploratory or reconnaissance surveys. There are two types of barometers : (I) Mercurial barometer (2) Aneroid barometer. ( I ) The Mercurial Barometer. Mercurial barometer is more accurate than the aneroid barometer but is an inconvenient instrument for everyday work dne to the difficulty of carrying it about, and the ease with which it is broken. The mercurial barometer works on the principle of balancing a column of mercury against the atroospheric pressure at the point of observation. There m two main types of mercurial barometers - Cistern and Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 2!19 LEVELUNG Siphon. In the Fortin type of cistern barometer, the cistern is made of a leather bag contained glass cylinder. The height of the mercury in the tube in a metal tube. terminsting into a level of is measured b / a vernier working against a scale and the readiug to ~\". The the mercury in the reservoir is adjustable by means of a thrust screw at its base- The mercury is completely enclosed, and by turning the thumb screw the volume of the reservoir may be reduced until the mercury completely fills it and the barometer tube. By this means, the instrument is rendered extremely portable. When the barometrical observations m in progress, temperature should be read on two tlteromometers. Barometer. The aneroid barometer though less accurate than the (2) The Aneroid mercurial barometer is far more portable and convenient and is, therefore. used almOSt exclusively in surveying. It consists of a thin cylindrical metallic box about 8 to 12 em in diameter hermetically sealed and from which air bas been exhausted. The ends of the box are corrugated in circular corrugation, and as the pressure of the atmosphere increases or decreases, they slightly approach or recede from each other. This small movement is magnified by means of a suitable lever arrangement and is tranSferred finally to a pointer which moves over a graduated arc. Fig. 9.54 shows the essential parts of an aneroid barometer. The general external appearance of the aneroid barometer is shown in Fig. 9.55. 6 11 n5 ginee 7 rFIG. 9.54. DIAGRAMMATIC SECflON OF AN ANEROID inI. OUTER CASING • . UN!< g7. SUPPORT fUR SPRIN~ .IO.CHAIN nBarometric Formulae etLet it be required to find ~ CORRUGATED BOX 3. SPRING 5. KNIFE EDGE 8 HAIR SPRING 6. POINTI:R l l SCALE. 9. VERTICAL_ SPINDLE the difference in elevation H between two points A and B. Let d. = density of air at A d = density of air at any station h = height of mercury cclurnn of barometer at any station L = height of the homogeneous atmoshphere on the assumption that its density is constant throughout having a value d. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING 2SO p = pressure at A in absolute units g = acceleration due to gravity h, =barometer reading in em at the lower wThen station A h, = baromelric reading in em at the higher wL =-p- d,. g station B H =difference in elevation between A and B, in metres. wIf g is taken constant, : p=L.d,g=h.d.g ... (1) or .EBh = . . . (2) law <·Hence, is constant by Boyle's Let a(h- Bh)d. g=(L- BH)d,. g and hence L will be const'ant. or sBh.d=oH.d, FIG. 9.55. ANEROID BAROMEI'ER or in altitude of BH yEBH for a small •difference change in baromelric reading we have at a distance BH above A, f., nH =L=Bh . d = ~ from (I) da .h,'- ' h, hdh = L (log. h, - l o g , h2) (2), wRe edguecting this to common _logarithms and substiruting the numerical value of L from (at 32° F and 45° latirude) H = 18336.6 Qog10 h, - l o g \" h,) \".(3) Applying a correction for temperarure, we get JH = 18336.6 - l o g , h,) [/ 1 + t, + h - 64'\" \\ ... (4) 900 (log\" h, fbiwbnoaohrrtmehotrhmueefleaoBtrmeort:em,hrtt,c,eatur==,ncryuttaeernaimmaddaltpdpeietbt,trrihaaaoerrranouuramerrlteewemotcooeoerffr,asrsteaaauactiisrirtreoiodnwniisnne.blylhTddaaeehsdsggeerrtfteeaoobeecrsharebFtodheFmaeahtehahralerperneniprcnemhlrhieoeoeriditemidtaedafbtiaotenatrrgrsAo.Bmai.nsTeyhtecerod.riarfbHefecoortveewendecveebxeyrp,oreftfhsosetrieomnmfopelealrorpcawpurlriuinieragesl h, = h,' [I + a (t,' - t , ' ) ] \".(5) where h, = corrected barometric reading at B h,' = reading at B at A t,' = mercury temperarure Downloaded From : www.EasyEngineering.net

) Downloaded From : www.EasyEngin25e1ering.net l.I!VELUNO t1' =mercury temperature at B a = co-efficient of expansion of mercury= 0.00009 per !° F The cotikted height h, is to be substiruted in (4). in degrees centigrades, I f the temperarures of the detached thermometers are measured T, and T2 , Eq. 4 takes the following form ...(6) .. ( T,+T,)H = 18336.6 Qog10 h, -log, h,) I +500 Another formula given by Laplace is in the following form I+ t , + t , - 6 4 ° ) ( I + 0.002695 cos 29 ) x log . . .. . h, . . . . . . . . .(7) H = 18393.5 ( 900 where 9 is the mean latirude of the stations. two methods of levelling with a barometer: Levelling with the Barometer. There are (I) Method of single oberservations (2) Method of simultaneous observations irdseuaerdaiknteog(In1n)tiahsttehMreisaaeckcthelhmwannedsgttahaetotsoidoef,naincSht;hintethghsetelaebtaibaortaOomnrmb.oosmeseTptreehvhtre{eeJrr/iejrsoiesnawcsdbaihrnroi:rcguihesgdhttthafukrboseamcokpblapttaocoienintehtddeutsoriitnnavrgpotoilnvitnghetepaaolinlinndttae.tramvTaohlssiepnbhgteeeletmrwicpereeerenaardrriuotnhrrgese ngineering.noptsttaemahibtrtmrkaees.rteveoeitoriBh.rbovnseyapuaI(TsIln2tsEBaieftslhm)bocoyxaietamnearahtosesoyMmisuec.smrrmtd.oleaeptuapmbeatmtslihdrtneeeToteipaoeirennhnraatrdoghegtr9rruiueeosn.ars2ddrdoengtetu4.ha,edoofc.emdfboepTiisSsnbprdohFteeitgsehimieramiemrnevndtaruooa.dvearilatnutlfatiiiigrmotuAetaeieoshnlozAsldbneaesnosopiorsseletwsubo:fheraesaawvieldtdtterboerhiovondtOmawtgba,tbehtbwsseieolaosittiormewtenotsrahIrimvetbr~enaa{eeoatalJeaniort/frtobtojeneeoaonamr7eTlttnrs,shh8oetsteo2hehe.mmmat0ceeerp2a:neraetosmsleatyetlberkae.rrcreasaaedrtsoemintoiknounmrdrevnrtsttnrepaahawobktaetdiysdBireoiotueunmhnfdc8etfisafeuer.kaealolwtAtidtaoinmaarO.cingnMtphhneb=aroe.oaettemhurdttor6hhoeserbob8oelmotyssaersfreporeerorohmbstlvemlioeyFomoarirfntwieficitetowliieadasntnrshorgc.ehiWpnbigasrtabnrdee:ereagacroankrvetamtaoesaumpltefsaitrtto:esoehntrmoaeass3ttrf, 78.28 em at 12 A.M. etTemperature of air = 72 o F Barometer reading at B : 75.30 em at 10 A.M. Temperature of air =50 o F Elevation o f A = 252.5 m Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 2.52 SURVEYING SotuUon. wt, 78.02 + 78.28 = 78.15 em. The probable reading a t A at t o A.M. = h , - 2 wwSubstituting Reading at B at tO A.M. = h, = 75.30 em (average), at A = -68 + 72 = 70\" F at to A.M. - 2 t, at B a t 10 A.M.=50\" F .= the values in formula (4), we get E:. Elevation of B = 252.5 + 315.5 = 568.0 m. H =. 1833.6.6 _(lo.g h,- log h,) ( I + t, + t,- 64) 900 a9.22. HYPSOMETRY 7 0 + 5 0 - 6 4 ) .= 315.5 900 son the fact that the temperature at which water bOils vades with the atmospheric pressure.18336.6(log78.15-log75.30)x(1+m yA liquid bOils when its pressure is equal to the atmoshpheric pressure. The bOiling point Eof vapour water is ·lowered at higher altitudes since the atmospheric pressure decreases·' The working of a lrypsometer for the determination ''(if· altitudes of stations depends nthere. A hypsometer essentially consists of a sensitive thermometer graduated to 0.2• F or 0.1• C . The thermometer is held uprighi' in a special vessel in such a way that its bulb is a little abOve the surface of water contained in a small bOiler. A spirit tamp is used to heat the water. Knowing the bOiling temperature o f water, the atmospheric pressure can be fouod either from the chart or can be calculated from the following approximate formula: ... ( ! ) Pressure in incbes o f mercury= 29.92 ± 0.586 r, where T1 = the difference o f bOiling point from 212\" F Having known the atmospheric pressure at the point, elevation can be calculated by using the barometric formula given in the previous article. However, the following formula may also be used to calculate the elevation of the point abi:>ve datum : E, = T, (521 + 0.75 T,) ... (2) Sintilarly, E2 at the higher station can also be calculated. The difference in elevation between two points is given by where .E= (£1 - Ei) a lcorrection = ... (3) a = a1r temperarure 1 + t, +, - 64) 900 where t1 = air temperature at lower station t1 = air temperatur~ at the higher station. Water bOils at 212• F (100\" C) at sea level at atmospheric pressure of 29.921 inches o f mercury. A difference o f 0.1 • F in the reading o f the thermometer corresponds to a difference of elevation of abOut 50 ft. The method is therefore extremely rough. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 2.53 LEVELLING Example 9.25. Detennine the difference in elevation o f rwo stations A and B from the foUowing observations ·: = 210.9\" F Air temperature = 61 • F Boilirig point at lower station = 206.5\" F Air temperature = 57\" F Boiling point at upper station Solution tower point abOve mean sea level is given by Height of £ 1 = T1 (521 + 0.75 T,) ; where T1 = 2 1 2 \" - 210.9\" = 1.1 • Sintilarly. £ 1 = 1.1 (521 + 0.75 x 1.1) = 574 feet. height of upper point abOve mean sea level is given by · r, = 2 1 2 • - 206.5\" = 5.5\" E2 = T2 (521 + 0.75 T,) ; where E, = 5.5 (521 + 0.75 X 5.5) = 2888 ft. t,-Air temperature correction 64 61 + 57 - 64 t, + =I+ 900 -1.06 =a=l+ 900 nglevel, . . Difference in elevation= H = (E, - £ 1) a = (2888 - 574) 1.06 = 2453 ft. PROBLEMS i Dumpy level, Y-level and Tilling level. n3. What are the different typeS of levelling staff ? Sti!te the merits and demerits ·of each. e4. Describe the 'height of instrument' and 'rise and fall' methods of computing the levels. eDiscuss the merits and demerits of each. S.(a) lllusuate with neat sketches ~ COD5auction of a surveying telescope. r(b) Distinguish between the following : !. Define the following terms : line. Redace,; Benchmark, Parallax, Line of collimation, Level surface, Vertical line, Bubble Dip of the horizon, and Backsight 2. Decribe in brief the essemial difference between the following levels: in(1) Horizontal plane and level surface g.6. ncross-sectioning. e7. Explain how the prncedare of reciprncal levelling eliminateS the effect of annospheric refraction tand earth's curvature as well as the effect of inadjustmenl of lhe line of collimation. (in Line of collimation and line of sight (iii) Longitudinal seclion and cross-section. for (1) profile levelling, and (in Describe in detail how you would proceed in the field 8. (a) R.L. of a factory floor is 100.00'. Staff reading on floor is 4.62 ft and the staff reading when staff is held inverted with bottom touching the tie beam o f the roof truss is 12.16 ·· ft. Find the height of the tie beam above the floor. (b) The following consecutive readings were taken with a dumpy level: 6.21, 4.92, 6.12, 8.~2. 9.81, 6.63, 7.91, 8.26, 9.71. 10.21 Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 254 SURVEYING The level was shifted after 4th, 6th and 9th readings. The reduced level at. first point was 100 ft. Rnle out a page o f your answer-book as a level field book and fill all the columns. Use rollimation system and apply the usual aritbmetical check. wthe (A.M. I.E.) win lndlcate the highest and the lowest points. 9. The following staff readings were observed successively wilh level, the instrwii<nl having moved forward afier the second, fourth and eighlh readings : been 0.815, 1.235, 2.310, 1.385, 2.930, 3.125, 4.125, 0.!20, 1.815, 2.030, 3.765. wB and .Obtain elevation 132.135. Enter lreevaedT1li0hn.ehgesCrfwioirnmesetplnearvereeathldeitbnhogefoirkrwsi-stfaeosramantandkd·aentnfhdaelwlreilmdlahuse/tc!t)ehlpoeto.dhi'senoiBtsflfe.fvreehdlesul.cdinAugpppolleynvetahlleinbgeunscnuhoamtlesacrhkwecioklhsf. Find also lhe difference EB.S. . the height of collimation melbod. a --3.92 It was required to ascertain elevations of A and B. A line o f levels was IBken from A to !hen continned to a beDobmark of elevation 127.30 ft. The observations are recorded below. the R.L.'s o f A and B. s7.05 y2.36l.S. F.S. _,R.L. E4.81 A 1.46 7.78 n8.63 3.27 B 0.85 2.97 7JJ2 3.19 4.28 127.30 B.M. (A.M. I.E.) staff l l . The following consecutive readings were taken with a level and 3 metre levelling continuously sloping ground at a common interval of 20 metres : on 2.722. The reduced rleevaedlingos0f..6t0hC2e3,kfui1rlas.2tte34p.othineJt.gr6weQda,us ce21d.5972l.4e1.v2e2l0.s.2R3o8uf,lelh0eo.9u1tp4o,aint1ps.a9ga3en6d. of2a.l8sao72le,lvhee0l.5gf6ri8eal,ddie1nb.t!o!o?o4kf. and enter the above lhe line joining lhe first and the last points. 12. In runoiDg fly-levels from a benchmsrk of R.L. 384.705, lhe following readings were obtained. Baoksight 3.215, 1.030, 1.295, 1.855. Foresight 1.225, 3.290, 2.085. From the last position of the instrument, six pegs at 25 metres inteval are ro be set out of I in 100, lhe have R.L. of 384.500. Work on a uniformly fa11iDg gradient setting lhe tops first peg is to the given gradient. out the staff resdings required for on of the pegs lbtehaveceilspiagogh1fet3. .thfFoeTrihleiTesi.goBfhpot.lil.ottdhwiesiinlfagnnttcihsreeessiandignainvsgteqrsruuamaghneeatdnivtetie4sib0seaekannnnddoIwBak9pnep0nltyomfrolehhmtaerevseuthsearuenasplpaeegclcehetvievacoetkeflsyd..ancAoollslliodm. altecivaolenclulebarotreookr.lhoeRfecc3oo0rn\"restcratuencddt Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngi2n5e5 ering.net LEVELUNG Point B.S. /.S. F.S. Rise Fall R.L. ' ReiiUlrl:s I 3.125 1.325 B.M. 2.320 ' 0.055 ' ' T.P. 2 '' ' \\ 3 ' 2.655 2.165 125.005 TP. 4 ' 3.205 T.P. 5 3.625 125.350 1.620 X T.B.M. I6 122.590 7 8 14 (a) Differentiate herween 'perrnanem' and \"temporazy' adjUstmentS o f level. due to each (b) Discuss lhe effects of curvatUre and refraction in levellillg. Fuxl the correction and the combined correction. Why are these effects ignored in ordinary levelling 7 .sw1e.a6ts6u4p!.heInSFne.uaxmrIlnoAvtheleeadvnedaalulnitendhgedsheisfttefarefwurfepenercenenaedtaiiwnnrgosBle,povoneitnhl teAsofraAensAdpaencBadtnivdw8e eBrs.eotnaf2f.o6p4rpe2aodsaiitnnegdss3ido.2en2s8AofmaanrdesripBveecrt,wiveelrlheye. level was The level 1.086 and 16. The following notes refer to reciprocal levels taken witb one level: Staff Reading on Remarks lnsrrwnenJ i QNear P Q Dismnce PQ = 1010 m i p 1.824 2.748 R.L. of P = 126.386 n Find (a) ,, gstation 0.928 1.606 iheight I neeityhsaerdvsilsigiabh1blte8-oh.vojeuuTssoMte .aSaab.nLodpv.eerlishfotehnle.bts:shhtiadopner.diczikonMngoa. fkoeTnWheelhlheseih.Leinipdgeehcicsetkss9oaofryyfathraedassssluhaimgibphop,tvtieoainnMsl.ilg.hShe.tLl.if,grohwmt-obroktuhseoeuttiospthekondofiswLanaJJl.itcgoehtbbeelbwo2eu3cs3neforcurvatureandrefraction.and lhe aue R.L. of Q (b) lhe combined correction (c) the angular error in lhe collimation adjUstment. horizon at a certain is 40 km. Find the 17. A luminous object on the top of a bill is visible just above the the sea-level. The distance of the top of the hill from the station at lhe hill. IBking the radius of lhe earlh to be 6370 km. of r19 idetermine ngin of a level tube. Describe bow you would attached to a dumpy level. .point (a) Exaplain what is meant by the sensitiveness in the field the sensitiveness of a level tube n20. What are different sources of errors in levelling ? How are they eliminated ? mbe has a sensitiveness of 23 seconds for 2 mm · division, find the error a distance of 300 ft caused by. bubble being one division out of centre. et21. Describe with the help of a sketch, the working of an aneroid barometer. the (b) I f lhe bubble and at lhe staff reading at (U.P.) (c) Find lhe error of reading of levelling staff if the observed reading is 12.00' sighted lhe staff is 6\" off lhe vertical through lhe bottom. 22. (o) List out carefully and systematically lhe field precautions a surveyor should IBke to ensure good results from levelling field work planned for engineering purposes. (b) A 12-mile closed levelling traverse reveals a closing error of 1.56' on the starting benclunark. Would you consider the work acceptable ? Give reasons in support of your answer. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net - .. f SURVEYING 256 23. (a) Describe briefly the temporacy adjustmerus of a dumpy level. w iA to levels (b) Two mile stones A and B are separated by 6 miles. A line of is run from B and then from B to A. The differences of levels are found to be (A.M. I.E.) w8. A to B + 181.34 ft. w9. BtoA - 180.82 ft. Do you consider the levelling job of an acceptable quality of engineering work ? ANSWERS .10. E185.3621.1. (a) 16.78' (b) Highest point : Second (R.L. 101.29); Lowest point : Fourth (R.L. 97.79) cbange points:- 1~1.775, 132 .700, 132.505, 131.505, 137.510, 135.355. 133.620 R.L.'s of as\"' Difference in R.L.'s : 1.485 m yl 1.000 116.75 ; IIS.77. 186.260. 192.122, 191.490, 190.864, 190.150 (T.P.), 189.474. 188.452, 187. 516 (T.P.), E2. 1.250 Gradient I in 23.82, falling. n3. I.SOO Peg No. Staff reading 12. 4. 1.750 5. 2 . 0 0 0 6. 2 .250 13. B.S. I.S. F.S. I l&e I Fail I _M,_ Remarks 1.800 B.M. Poinl 3.125 I U.i}jj 123.680 T.P. I I 125.1J91 2.265 1.325 I 0.735 I'I T.P. 2 2.165 T.P. l.Jai 2.005 i:bt.!i.SO J 125.353 T.B.M. 4 1.040 1.920 0.400 5 3.625 6 II II1.620 2.655 ] 124.615 7 3.205 -1- 122.450 8 J1.480 12.145 120.445 122.590 Correct R.L. of T.B.M.• 122 . 620 metres. IS. 0.582 m, full. ' ( c f + 11\" 16 (a) 125585. (b) 0.069 m. 17. 107.76 m. : (c) 0.81 ft. 18. 41.89 miles. 19. (b) 0.03 ft. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net [§] Contouring 1fIiOIosI0JrnJ.m[r1JeS.ap. rlTeTipnGhshleeeaEusnnstN,ve,odaEritlnhuRbeecAoaotLrmohteofloaphutpooirvlgraierznlaiopnnaheoltsirtaci.lrlumysduaeOrpasvsuetoyiwsf,oehblftlhiogettahhhsleypshoveoi,eernrnitztchsiocoarannuclctlaaoyelnu.drasbSieulfiwcnhtreehelselpmraaearsrsepeelsvantetmiearvtdroeiecsatbpklyonwcsooiiswtdnhieontarlnydoailnsougafs,rteeotdphhroeoegbcqrehpuacuoiparrieuhnedstissce.. they indicate the elevations directly. nginelIaTiittitsshthnheeeeniatssoonesfwllaoaCAaeiAtwsplloleoeiabcncvnwsattiOooeaetgeorntuapirlutnoierioonmsnertndgucreryaarabwsr,olptkoeyefhih,nssetiihcpc11iemhatt0hmnm1aaehstyn,.hha0iidlepmo0almbswnaeawospmsgpuatrhihnsreneufwedsaraarrreeerhscvnypeevwetrrsstayehaehlloesitleoneedeafywtenryhtsgcnaeim,aonrlnerongdaegiautnrhrrknoetragdheutprrehpnaeilcecariddpsoegtkurusnerpeaeroitisslsleonnau.euttnnneearnotdIdrn.iesffbndaeygjorFcatohltnwiyiege1tndhma.0itentlh0aseegebup.r1v0ywr0e0fm.tclaai1h,socatmeaeueprwtsrlospheehomeiovolenesfiewaravnlerstattakshshtnsm.ieeiuodatoranIfgfflifapolosrwcoorettmhesqnuihsl.ecdunlleraodaolbpAl.ewwetfi,oneaiIpcgotltfiheeoo,btcvrgntoaaawrtswnoiathlnithempauoooevethrwnuadeersi.prr.le.cs efeatures. ring.netlTocgchUIcofhofoirg.neunlth.thtn~t.ohloetcyueru.oTyr(rCmsniuhs)gtOaneToirpsisouNwshTuuvreiwiIhfenitJlOkraedaiintlmbctLliohlcceeniiwaoboosRraliemvrncftaoeumdem~lrhriaosie\"isogtistursaoefTlhnenooltdEayhckpfbudeeRe.rrilcopnaoVutlbpthtogkhnAeeese.oeddctrLenrwuoTi,lnzggecahtoserrotoeogtennonadurtunthae.oneantolaaudndtrcAr.eyifehzorqoFri:tunncwocoiottaovrtTeaohnanrlhetvelctoecreodvaouo.nuliensnrtrrcttysoadoe.inueinncncfprtautltoeeeanetnurptidrvvbdrvlaaeegsalntdrliwo,necu<uoptespeon;nehehortntndovohond,usaeuetsllrwrdnatwshoduei·sfbspeimosepeporfoaenocilntnlalhaalddtoeltsslhiowenfepdlogtiautenenetrpgnscdvotoet,eagwnrmelcraoopooloiunntwsuhcnesarehosidpndrsenpweietsnhcerweioateaesceitrsfreulriaslovtnainattrtvchhbhslyee.ee:ee. (257) Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING 25~ (ii) The scale of the map: The contour interval should be in- versely proponional to the scale. I f . 10 ['l..i\"'\\.,:'' '''' '' '' '' '' '' :'' / rhe sCale is small, the contour interval 100 '' '' should be large. I f the scale is large, ' '·•· '' '' ·- the contour interval should be small. 99 '' 98 I :/ (iii) The purpose and extent '' 97 \"'\\.,: ; '' wof the survey : The contour imerval \"'\\...: '' \"'\\.,: iargely dept!nds upon the purpose 96 JDd the: c:xtem of the surv~y. For 95 wt!xample. if the survey is imendOO. 94 for detail«! design work or for ac- wcurate eanh work Lllculations, small comour interval is to be used. The .E vextent of survey in such cases will generally be small. In the case of a: v 'lm:ati.m surveys. for lines of com- munications and for reservoir and v sdrainage areas. where the extent of ysurvey is large, a large ContOOrT\"; terval is ro be used. E(iv) Time and expense of field nand office work : If the time available is less, greater contour FIG. 10.1 inrerval should be used. I f the contour interval is small, greater time will be taken in the field survey, in reduction and· in plotting the map. is these aspects. the contour interval for a particular coruour plan the Considering all interval is kept constant in that plan, otherwise it will mislead .~elected. This contour the ground. The following table suggests some suitable values of general appearance o f ~amour tmervai. I Scale of mop Type ofgrou11d i Contour ltrJervJil (metres) (l cm=lLOam\"'' or less) - ;: Flat -I 0.2 to 0.5 .. Rolling 0.5 to 1 l ! ~ Hilly l , 1.5 or 2 r· Flat l 0.5, l or 1.5 - Small fl em= 100m or more) Rolling ·~ I. l.5 or 2 IJ Hilly_ I 2. 2.5 QC 3 Flat 1. 2~0or5 3 Rolling 2 __ _ ___ 1 Hilly Sto!O Moumaineous 10, 25 or 50 Downloaded From : www.EasyEngineering.net

CONTOURING Downloaded From : www.EasyEngin2e5e9 ring.n.e·tjj' ~~ 'the values u! of contour interval for various purposes are suggested below H,,. Scale Interval (meues} em = 10 m or less 0.2 to 0.5 'h e m = 5 0 m to lOOm 0.5 tu 2 L 1'' ···Icm=50mto200m I 2 to3 For general topographical work, the general rule that may be followed is as follows: · Contour interval- No. 25 per km (metres) of em or No. . 50 . (feet). of mches per mde 10.3. CHARACTERISTICS OF CONTOURS I The following characteristic features may !' t c used while plotting or reading a contour I' plan. ,, I. Two contour lines o f different elevations -'~ cannot cross each other. I f iliey did, the point n Fig. !0.2). I 2. Contour lines of different elevations gcan unite to form one hne only in the case 1 ofm:.: :.«::non would have two different elevations However, comour lines of '~ which is absurd different elevations can intersect only in the iof a vertical cliff. case of au overhanging cliff or a cave (See n3. Contour lines close together indicate ethey are far apart. If they are equally spaced. eunilonn slope is indicated. A series of straight, rparallel and equally spaced contours represent a plane surface. Thus, in Fig. !0.3, steep slope inat B·B, a unifonn slope at C-C and a plane surface at D·D. steep slope. They indicate a gentle slope if 4. A comour passing FIG. 10.2 gthrough any point is perpen- in represented at A-A, a gentle slope _,__._dicular to the line of steepest nslope at that point. This agrees 'B ;c ,o 90 t:::- ewith(3), since the perpendicular -------,';' - ' 80 distance between contour lines ; 70 '0 60 tis the shortest distance. ~c td) 90 'A - - ' . _ 80--j.___-- !. ----.;__ s7o1-Y- r--!------ ;''e ;' iA 5. A closed contour line {a) {b) (c) ~ith one ·or more higher ones iitsi~e it_represents a hili [Fig. FIG. 10.3. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 26(\\ SURVEYING 10.4 (a)] ; similarly, a closed conrour lhe same elevation cannot unite and w @)continue as one line. Similarly, a single contour cannot split into two wlines. lbis is evident because· the · single line would, olherwise, indicate line with one or more lower ones 100 inside it indicates a depression wilh- out an outlet [Fig. 10.4 (b)]. 6. To contour lines having wa knife-edge ridge or depression which does not occur in nature. .However, two different contours of Ethe same elevation may approach very near to each other.(a) (b) aof lhe mar FIG. 10.4 .. s8. Contour lines cross a watershed or ridge line at right angles. They form curves yof U-shape ~round it wilh lhe concave stde of lhe curve towards lhe higher ground (Fig. 7. A contour line must close upon itself,. !hough not necessarily wilhin lhe limits 10.5). ;., -:; \\)95 E9. Contour lines cross a valley line 100 '•'' at right angles. They form sharp curves w A1oo nof V·Shape across 1t with convex side o f lhe curve towards lhe higher ground (Fig. 10.6). If !here is a stream, lhe A s scomour on either side, turning upstream, . 90 may disappear in coincidence with lhe ~85 ~90edge of lhe stream and cross undemealh the water surface. ~80 J >;::__10. Th~~~ contour appears on ei.!!J.er sides of a tidge-or valley, for ~80lhe highest horiwntal plane chat intersects lhe ridge must cut it on bolh sides:· The R;dg~ 85 / ~-~~.lleyline ''· same is true of the lower horizontal plane • .of!G. 10.5. FIG. 10.6. chat cuts a valley. 10.4. METHODS OF LOCATING CONTOURS o The location o f a point in. topographic survey involves bolh horiwntal as well as ·vertical conrrol. The melhods of locating eontours, lherefore, depend upon lhe instruments us~. In general. however, lhe field melhod may be divided into two classes : (a) The direct melhod. (b) The indirect melhod. In lhe direct method, lhe contour to be plotted is actually traced on lhe ground. be plotted. After having surveyed chose Only rlwse points are surveyed which lwppen ro points, !hey are plotted and contours are drawn lhrough !hem. The melhod 1s slow and tedious and is used for small areas and where great accuracy is required. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 261 CONTOURING In lhe indirect method, some suitable guide points are selected and surveyed ; lhe guide points need nnt necessarily be on lhe contours. These guide points. having been ploned; serve> as basis for lhe interpolation o f contours. This is lhe melhod most commonly used in engineering surveys. Direct Method As ·stated earlier, in lhe indirect melhod, each contour is located by determining lhe positions of a series of points through which lhe contour passes. The operation is also sometimes called tracing out contours. The field work is two-fold : (!) Vertical control : Location of points on lhe contour, and (il) Horiwntal control : Survey o f chose points. (i) Vertical Control : The points on lhe contours are traced eilher wilh lhe help of a level and staff or wilh lhe help of a hand level. In lhe former case. lhe level is set at a point to command as much area as is possible and is levelled. The stalf is kept on lhe B.M. and lhe height o f lhe instrument is determined. I f the B.M. is not nearby, temporary benchmark (T.B.M.) in chat area. , 101 fly-levelling may be performed to a ~ I ·Having known lhe height of lhe instrument, lhe staff reading is establish ~--..___calculated so chat lhe bottom of lhe stalf is at an elevation equal n strument is 101.80 metres, lhe glhe contour of 100.00 metres will ··\\.~\\ to lhe value o f lhe contour. For ibe 1.80 metres. Taking one con- ntour at a time (say 100.0 m con- tour), lhe staff man is directed eto keep .!he staff on lhe points · example, i f lhe height o f lhe in- stalf reading to get a poinl on eon contour so chat reading of '·,·, r1.80 m is obtained every time. ·•. ·•. iThus, in Fig. 10.7, lhe dots rep- 98 nresent lhe points determined by this melhod explained above. FIG. 10.1 If a band level is used, slightly different procedure is adopted in locating the points gon lhe contour. A ranging pole having marks at every decimetre interval may be used in conjunction wilh a n y type o f hand level, preferably an Abney Clinometer. To start wilh, .na point is located on one of lhe contours, by levelling from a B.M. The starting point , must be located on lhe contour which is a mean of chose to he commanded from chat eposition. The surveyor chen holds lhe hand level at chat point and directs lhe rod man ttill lhe point on lhe rod corresponding to lhe height of lhe instrument above lhe ground is bisected. To do this conveniently, lhe level should he held against a pole at some convenient height, say, 1.50 metres. I f lhe instrument (i.e. lhe hand level) is at 100 m contour. the reading o f lhe rod to he bisected at each point o f 100.5 m, wilh lhe same instrument position, will be ( 1 . 5 0 - 0.5) = 1.0 merre. The work can lhus be continued. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 262 SURVEYING The The s1aff man should be iostructed to iosert a lath or twig at the point thus located. twig must be split to receive a piece of paper on which R.L. of the contour should be written. www.ToabAtishyfheseouaaofinprlfedtaoftaA(asIbIiainnesnllvf).BetsttsesmetrFhrcFHsaiewfooegolrohlnno.hrrdatmiimrincvvor1tsh>aieahlmn0tcyenutg.thas7lrmleylel,lmbcisa,looetytesenachtCutmhartheraoeeotbvo.eauneeddp,rtypTt.sroh·oothicetiitnlheewnohlatidedntsanossdioenyl\"spsbims.sthoytteusehoai\"rnumyewvItr·aoesnvnryboeteotyotarbhpaniaynealbvorgrweetccvidroaoeassoatmrmsreuektdisrodapovgyuapsoeehshsftynfeisaorbiedvnswcerletgoaoandlrnrlaugebytntopseebhdeaureeyowdnrnssdtopen,hcsralaseakhntunpntumadhroerisveenasiiyenr,uitnnythtrasudleveaya.bldoerlllayeelpotHneerwonaeddoritovionrwtutehatbhlsrseviybeslnveyereeeremttssrsh-y,.eampsepo.yueeaircnysfvtabaeemenyttbhodeeeeldoloecppucxwaoawasttrieoietntinednytrtdhgk.st. EasyttiohneeirrbpeoelIIallnneroivdcoaitanhrtt.eieioscdnt.TsmhWMeeatshrheeeotilhdego,fuodiuissndnoteedmr.pepooTlgiahnuteitinsdgep,aorpieinottisnnistosarr,aaesrseeuxtmhcseeeenpdletcpttbhelodyattteacdtlhooeinnagcnsidld·oe~p.nce:oc;nesby.tosetutepwrmoseienonatfsresatonrntyahigentthwhteodlricnaaoewdnsjnatoca·uebnnrdyst guide points is unifonn. EThe following are n(I) By Squares (Fig 10. 8) points 'orne of the indirect methods of locating the ground The method is used when the area 10.4 : ro be surveyed is small and the ground ----r10.6 is not very much undulating. The· <l!ea ro be surveyed is divided into a number of squares. The size of the square may vary from 5 to 20 m depending upon lhe narure of the contour and contour interval. The elevations of the corners of the square are then detertnined by means of a level and a staff. The contour lines by interpolation. It may then be drawn the squares may be is nor necessary that oathrfeertehaelasroesauamspeepdresicizniea.bplleaScobemreoeatfkimssqeisun.atrhreeesc. slauWnrfghalecenes between corners, guide points in addition ro those at comers may also be used. The squares should be as long as practicable, FIG. 10.8. SPOT LEVELLING. yer small enough to conform to the in- as equalities of the ground and ro the accuracy required. The method is also known spot levelling. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngin26e3ering.net .I \"joocaatp1hrrbnfo0oadri.stunct9shpatt,-shetnsth(lIeeatTyniehcllsm.)hreeuteiletareoehavrBrnvspikeiessysao.eyatdidim.imnnoe'uChtepnsneT!wrertleohmhafnoimosveotdfeshridmsa-tntehsn,creaeekrouxstccocedhplhssrdioolosDooomdn-psrnpsnwsoaee-stiiyicsohnsttetnhhetibcoemeti.nicSdto~wshoopfnmIaiusterssrrtsse\\a·sahtn.rcsaoakutrur~eeceieT.tl.trdrw.da.oh...rb.ootes.u.hl.Tsb.enf.e-.e:hcspl teerohftpocrmoeiaontscrinsooitotns-srnensiretvtarseoeroicalrucantwsaiilrrneoocea,tnslt1yuwietnoatltohehyalrlseneoytdhusaaiceptdprseoeatjouhanccir\"cenetesivo\"neundte'nsut1rtpyertvrroeewepidinciynhoinlotsteiletsnai.nrenrteetrpeovcTod!uaatothlhhlnrafeo_seet_.neaatdlnshfcTtpdio•hreanohnloecdatutnhiodasnibeu,s,g1wecsr1supohrianmoupni.li.crlfteJlpoopwuFttuortitathivoershgyseedene..CONTOURING also be used in the direct • method of contouring with a slight modilic\"ation. In the :..,! ']•' \"I' I'\" \"~ :\\ \\!- .1 ! 1~ method described above, ! points are laken almost at !I regular intervals on a cross~ [! section. However, the contour ~ points can be located directly I! ngineisiapimbsfnlloaelsatifhtny1feest0caush1dibhcso.Ieeh8ofsi0oegpftnlfphlhoaoatdeccnfiraiaoeinefdtrtdffetsesdtatriahreofneeannooyrtinneitiorsrscieieniot1osvnrgncn.uet8lueetmrir0nolreaatuqaelnrcnrtuimeoitstgoidinre,nuietsaoiaddtuareieoenrnttdohcpdtearhoroenateirtsdlnealsttrcs-shmuelttaihrhnnifoeneeaasnnesced.9ec0toohpI°bnnfefoietriottsnwrocuatetrnsreqooeoutsnthonwishref-eeistlrwdelo1,m,cno0tbe0aiasoecisonnrcmmoroiseo1nsnsoiso-nslonei-t1n.lhtfih0enetahs0teht,emdeatiagrhdncerecddrocoiotutmissnotslhamodn-lfeua,iefnnlrt.htehrgsoeoeuTdani.dhmdlieeenaavygnpegsoloultaiihinnoldestgneors on the cross-section as in the FIG. 10.9 I: direct method. For example, i e(iii) By Tacheometrie Method rIn the case of hilly terrain, the lacheometric I.', i1acheomerer is a theodolite filled with r, :, [! n \"s1adia diaphragm so that slaff readings A g ifagaiost all the three hairs may be laken. The slaff intercept s is then method may be used with advan1ages. .nob1ained by taking the difference be- i eand bottom wires. The line of sight tcan make any inclination with the v ltween the readings against the top horizonral, thus increasing the range 14-----o .1 of instrument observations. The hori- zontal distances need not be measured. FIG. W.lO since the tacheomerer provides both Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 264 SURVEYING horizontal as well as vertical control. Thus, if 9 is the inclination of the line of sight 10.10), the horizontal distance (D), between the instrument and the difference in elevation (V) between the 'instrument axis and the point sight against the central wire intersects the staff are given by wwhere K1 and K2 are instrumental constants. with horizontal (Fig. staff, and the vertical in which the line of wpoint from which greater control can be D =K1 s e a s ' S + K,cos 9 and V=Dtan9 obtained. wdifferent The tacheometer may be set on a .Ebe taken on levelling staff kept at differeiit Radial lines can then be set making angles with either the ma~ti~· ,, aapproximate vertical difference in elevation meridian or with the first radial line (Fi'g. · sthe contour interval. Thus, on the same 10.11). On each radial line, readings may yradial line, the horizontal equivalent will points. The point must be so chosen that Edifference in elevation of which is greater between two consecutive points is less than nand vice versa. be smaller for those two points the vertical To sorvey an area connected by FIG. tO.lt smlAttihaentcraeehiyseeehsaobocameohrnifezdrtothrutniainctlthvla,oeelcfrtokhscperesomo,nitsuntaatrltacoasthteliaeocconbhaam,eennioednsmtegrtvhieeceetnerrnntiatcertlirarbetvererdelaay,rdvspieeaalorolnsbstedtttleaainditntie.ohesnedTsmhcbbaeoyyenitneotbhglueeervcsarhttuaioconcsanhenneinoombafvteeatesreaoiirnoc.mutheseTrphpcdoeooilriamnettetcmrdtaiavoisnenardsssicenaa,gulscsutuphrlaoeaelstq.eiutrdiaiqrdenibdasy.,l W.5. J.NfERl'OLATION OF CONTOURS Interpolation of the contours is the process of spacing the contours proportionately between the plotted ground points established by indirect methods. The methods of interpolation are based on the assumption that the slope of ground two points is uniform. between the The chief methods of interpolation are (1) By estimation (ii) By arithmetic calculations (iii) By graphical method. (I) By Estimation This method is extremely rough and is used for small scale work only. The positions of contour points between the guide points are localed by estimation. (il) By Arithmetic Calculations The method, though accurate, · is time consuming. The positions of contour points between the guide points are located by arithmetic calculation. For example, let A. B. D Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net CONTOURING 265 and C be the guide points plotted on the ~·:' &· map, having elevations of 607.4, 617.3, ' 612.5 and 6(}4.3 feet respectively (Fig. 10.12). Let AB '= BD = CD = CA = I inch on the plan and let it be required to locate the position of 605. 610 and 615 feet contours on these lines. The vertical dif- ference in elevation between A and B is (617.3- 607.4) = 9.9 ft. Hence. the dis- tances of the contour points from A will '! ------·-c!~!! ~''\\~ be: l~;,~-,- Distance of 610 ft contour point ~. ' = 9I.9 x 2.6 =0.26\" (approx.) point : [ 1 ' \\; ;.' ~ •' .:~-·-----I Distance of 615 ft contour q->·+1' ··'&·-·-·-·-· ·-·-S·O:\"•~~__ .! ~\\Gf 9 9= ~ x 7.6 =0.76\" (approx.) ___uoS n (ii1) These two contour points may be FIG. 10.12 located on AB. Similarly, the position of g In the graphical method, the interpolation is done with the help of a tracing paper the contour points on the lines AC. CD, Contour lines may then be drawn through BD and .also on AD and BC may be located. inFirst Method appropriate contour points, as shown in Fig. 10.12. By Gmphical Method elines eeach rline or a tracing cloth. There are two methods: iand let it be required to interpolate nCOD!Ours of 99.5, 100 and 100.5 oafTfrifehthtehderalfiiwnrdsenitagpmmraaaermyathl,loebdlseotoismpeariadelclpeuhasrthoeradethtaevedorien, risnatthyoeFaigrtterpaa1rnce0ins.ie1gnn3tte.crlvoeOaatlhnch,reaprmereppesirteerecenseetimninogtfea0rnvt.r2aalec.mlienvegatLrteeico.tluoItthfheo,rfeqsbe9uov9itrteoerdmam.l gB having elevations of 99.2 and 102 .100.7 m respectively. Keep the trac· ning cloth on the line in such a 105 etparallel representing an elevation of m values between two points A and way that point A may lie on a 101 99.2 metres. Now rotate the tracing 100 cloth on drawing in such a way that point B may lie on a parallel esenting 100.7 metre: points at which the parallels rep- FIG. 10.13 resenting 99.5 (pointx), 100.0 (point Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING '!66 y) and 100.5 (point z) may now be pricked through the respective positions o f the contour point on the line AB. Second Method . length is taken on a tracing cloth and divided into several pans, each repre- wsenting any particular interval, say 0.2 The second method is illustrated in Pig. 10.14. A line X f o f any convenient m. On a line perpendicular to X Y at its mid-point, a pole 0 is chosen and wradial lines are drawn joining the_ pelo·· 0 aod the division on the line XY. l e t - wthe .line representing one metre interval may Ebe made dark. Let it be required to interpolate contours of 98. 99. 100 andbottomradiallinerepresenlanelevation / a101 meaes elevations between two points of 97.0. I f required. each fifth radial sA aod B having elevations of 97.6 and y101.8 metres. Arrange the tracing cloth on the line AB in such a way that the point A and Erepresenting 97.6 and 101.8 metres respectively. The n99, 100 and 101 metres intersect AB may then be FIG. 10.14 B lie simultaneously on radial lines points at which radial lines of 98. pricke1 through. Contour Drawing dcmasoulrsiarnowvadesi.ssnhAgtTooofwhftteehsdrtehisetchthoiacnecvnogoitnnuofntegiuotsaoruhmuirnrrltiieetnlslirienpncseoellsieslk.aasehrtmelotydhraueoyltdafhrdfobeusemb,ncedodeanrrtmiecantsow.ekt.unenrtdoiatptl(hoiirntsiophnuertpeosgirphtfebheefeneaetttrhirwueaersbeiebrleslean.occfoktaTorrchenooeusenrpsttewovobanuorlbdrurorkiewnolgwionno.fnecfsgoIitunfnhmitekdot.ueuhsfcretop0rpnocbotioonetihnnutsettr,boss.oucsrromsnWhneoopthoouliautillhndner be written in a systematic and uniform manner. 10.6. CONTOUR GRADIENT faolepLirttoshhqoofeceecumitanocaltotllnegsiactslramAoaCtottaotphu,biponneepneentgtowddhtoci.iteirnnioutetlhtchalnrqThtletiueohgmnttiihuheraargcaeaeerntohyiddcontgihlntteiioarenbonntaroluecofttpgdorlmeiiitentteshortgenaahaeftrttaseceiiaisoredloaiylnhnibienbioscsaneirtelolshtoiirelnfteclcvohcyooaenteimet1nnofrtnedia'gtnsdeeollti.udmentbemhr,reyIyo.riafetvo1agpheTu0trtehdhig0achrseiedh.lesiointdoeiouAnodlcinnirtclmintenistlnecohcioetnotonhuettehaemesfodtesrtipf,heeroiomdtenbneaisycprnaislgopeitiutnnrhhftirhssatesfoo.seatootiuhnrhcodceeoeTnoohlbohdlhboinsnetataeIeeafvarxitivnltpthntiohieenongeerAdreianrga1tttagiraoais0cronnlo0ileuddtsgemua.vninrevdogiat(dlsetvhPenst.naeeatoim.gnnntlThd.iuiaainntyephtspegpre1er0bodageop.erfigms7rfroeeeoh)ierdud.cnmestvostihtiiieggwTnooodhhgnodinna.stt Downloaded From : www.EasyEngineering.net

CONTOURING Downloaded From : www.EasyEnginee26r7ing.net obtained in a similar manner. The line between any two pegs will be paraUel to the line of sight. omsgtnraeaftdfrtiehesenk.IetfpcTotoahfneat!ot~1ivrleretilhanedgiisrn1afg0diur0iSse,eotndntw.piotlaolTinnhot6leo<th;cieaslr1tee.v2tepa1tlkeheg+enis.0Bc.os2en0F(ttsooa=urayrt)1n.4gaud1rmiascdetomairemniecnttamtr,le2as0ni.etdxiTaminsmogepntrllopeoetos,csanitftleeireooctnemtshtsehaaeAnrydp, oreitwrnoaetdiatisdhnBeignt. agtthbhceeoeonnls1etto.vta2huef1erlf chain or tape (with zero metre eod at A) and moves· man holds the 20 metres end of metres. Thus, from one single instrument station several · till the reading on the staff is 1.41 points at a given gradient can be located. The method of calculating the staff readings through numerical examples in Chapter 9 on Levelling. for several pegs has been explained 10-7. USES OF CONTOUR MAPS The foUowing are some of the important uses of contour maps. 1. Drawing of Sections y From a given contour 105, plan. the section along any given direction can be drawn 100 to know the general shape 95 of the ground or to use it for eanb work calculations for a given ·communicaticn line in the direction of the section. Thus, in Pig. 10.15 (b), let n ait be required to draw the gsection along the line AB. iThe points in which the nline AB intersect with various econtours are projected on the axis OX and ~ir correspond- eing heights are plotted along rthe axis OY to some scale ito get the corresponding con- ntour points which may be gjoined to get the configuration of ground surface [Fig. 10.15 .(a)). 001 ~0------------~~~~~~ti-on-alo~n-g~A~B------------Jx § !2 ;g~o 8m co .... U) \"' 0) Q) ... ............ .-0) ..... -·-·•·-·-·-+-·t-+-·.,.8 FIG. 10.15. n2. Determination of Intervislbility between two points etbmtoeafpolertemTiasthyeelbebecdetiisrneutgaqsneucdtiheresetdiorbtedoptewotsedeireetmitnoeinrnmtehiienttehteirsitahinnengteeucirnelvatsietssiraoivbrnyiisliitbsyttioalittoiyodfnetsotehfremarthietnreieagnpegtonhuieenlraitarstliloyiAnntessaertnvavditesiroiabnBlisl.itkiyniF.looFmrAigee.trxceao1smn0t.pao1lnu6edr,. their elevation being 70 and 102 metres respectively. Downloaded From : www.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

I[Downloaded From : www.EasyEngineering.net i 268 SURVEYING Draw line AB on the plan. The difference in elevation o f A and B is 102.0 - 70 = 32.0 m. The line of sight between A and B will have an inclination 32.0 metres in a distance w J --~·--! AB. Mark on the line ·or AB, the points o f elevation o f 75, 80, 85, 90, 95 and 100 'the corresponding points in metres. by calculation. 70 A (70) Compare these points with i------t---------80~E the line of the sight will whave an elevation less than which the contours cut the ' 75 line AB. Thus, at the point 80 metres while the ground w --~------------------has an elevation of 80 me- ! 75 0 ·f. ,:I :'1 ~ 1 85 tres. Thus, there will be / \\ .Aan obstruction and points A 85 E -and B will not be intervisible. c -:The points C and D at which cl-./--~!--1-!--~!----- as -:il. Una ol sight ''''''''''' 90 90-~1- 95 95--+- ybe seen by inspection that /, Eall other points are clear nand there will be no obstruction at other points,.~!' the line o f sight and the .j i I' :I''' ;::s~:''' eR ~ 100 ground are at the same ele- 100-----l- vation can be located. It will ' 6 !to2) PIG. 10.16 range CD. execpt for the I 3. Tracing of Contour Gradients and Location of Route A contour plan is very much useful in locating the route o f a highway, railway, canal or any other communication line. Let it be required to locate a route, from A to B at an upward gradient o f I in 25 (Fig'. 10. 17). The contours are at an interval o f 99 m 1 metre. The horizontal equivalent will PIG. 10.17 therefore be equal to 25 metres. With A as centre and with a radius represenling 25 metres (to the same scale as that o f the contour plan) draw an arc to cut the 100 m contour in a. Similarly, with a as centre, cut the 101 m contour in b. Similarly, other points such as c, d, e.... ,B may be obtained and joined by a line (shown dotted). The route is made to follow this line as closely as possible. 4. Measurement o f Drainage Areas A drainage area for a given point in a stream or river can be defined as the area that forms the source o f all water that passes that point. A contour plan may be used Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net CONI'OURING 269 to trace that line separating the basin from the rest of the area. The line that marks the limits o f drainage area has the following characteristics : (1) I~ passes through every ridge or saddle that divides the drainage area from other areas. (2) It often follows the ridges. (3) It is always peipjlndicular to the contour lines. Such a line is also known as the water-shed line. Fig 10.18 shows the drainage area enclosed by a line shown by dot and dash. The area contained in a drainage basin can be measured with a planimeter (see Chapter 12). The area shown by hatched lines gives an idea about the extent o f the reservoir having a water level o f 100 metres . S. Calculation o f Reservoir capacity The contour plan may be used to calculate the capacity o f a reservoir. For example, let it be required to calculate the capacity o f reservoir shown in Fig. 10.18, having water n'<\" gineering.net PIG. 10.18. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net ~~' SURVEYING 270 beetwhqlyeieulvlaaalvtoitohtplTounelhnamtunohesifebm, eb1eaie0tvfete0werq..rA0eua0e1gaT,nlehAme2ttaeho,rteervea.otss.ohl..ute.ho.mT.ef.hrse.ue.thm,toweafAroetonwawfsoauaetrtcnehceccroeelonstbssthvoieeevoudtewlrusaeimcnreoemnean1ssut0ol10tubi0e,pren0lst9ciwel0modce,saeennb8day0nb.td.bhet.hye.e.9c.a0svcluccaooucrmnncilotaetouotsuceussdorirvn.sceitnooTmntuechtarrooeyvnuawtrtbloso.ieultlarSamlsin.tmhedvaeoislnlauhurrmlebydiee,s contour interval, the reservoir capacity will be given by w. V =~~(A,+ A,) by trapezoidal formula wwand .EPROBLEMS V = l: ~ (A 1 + 4A, +A,) by primoidal formula of Volumes. Chapter 13. For detailed study, reference may be. made to Chapter 13 on calculation 6. Intersection or Surfaces and Measurement or Earth W o r k : See a1. Describe various methods of contouring. Discuss the ,.~erits and demerits of each. s2. Describe with the help of sketches the characteristics of contours..•' y \"'3. What is grade contour 1 How will you locate it (a) on the ground, (b) on Ill.:. map. En5. Discuss various methods of intcrploating the contours. 4. Explain, witlt sketches, the t!Ses of con_tp,ur maps. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net [(m Plane Table Surveying 11.1. GENERAL: ACCESSORIES tpcahaloeordrttyignrrrgoPaitunlsapnsnrcdooericwbectineaandbnglcinsobfiginmeetlrudoislslteaennansoeytoesgbustrey.samlpyIsh.tthiceIcbataylntiosmptrbomeieagthenraoagunpdussheladeootrifoftnoasmoudatroivkereiwnytgtiortahpiavnoceugrmtrwsaeaphinnbicutyaehsnrcdmrbtihpyeebtd.yieamxftieiaelsiplntdisentisgenopbsoctshfoeeonrvtlfrefaoivterileloedlcnsao.snwrddhainniltgdeo. Instruments used following instuments are used in plane table survey The having arrangements for (a) levelling, I. The plane table with levelling bead (c) clamping in any required position. (b) rotation about vertical axis, and 5. Compass. n 6. Drawing paper with a rainproof cover. 2. Alidade for sighting 3. Plumbing fork and plumb bob. g 1. The Plane Table iThree distinct types of tables (board and tripod) having devices for levelling the plane 4. Spirit level. ntable and conrrolling its orientation are in common use eThe Traverse Table : The traverse table consists of eon a light : rand can be Table. ing.nebtottfwhhoyruerom6ellb0eytohvewxuse-Jcemello7rsrieb5tnhiwgmns.s.cesaorcmteWTnirowe.hwnheT.eTsanihscbeloltaehnlmoebop(etsuFahepideignsp.eedcurto,h1nnes1dcnst.eh2rirsee)sttwisidg:tehaoi.tsbTeflnheTfeirashedeembc,taoaoybtlnhla-seflailbisn-xettadsan-btdshrloo-eoesfctoakmbtcaeeokatdyaedrtjrdoabawjiebonioiitnntnuiglttataendtbidhshoeoa.aarobridpozveouverntreuatrtsitattcuehilacdaelalpllybobaasyxsli4plit-s5iioatnhnnxdaed.lne-6ds0Wuopwchcpekiaemetehnnrt (z) the Traverse Table, (iz) the Johnson Table and (iii) the Coast Survey a small drawing hoard mounted rotated about the vertical axis tripod in such a way that the board can be by adjusting tripod legs, usually clamped in any position. The table is levelled tthus be oriented. (271) Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net SURVEYING 272 The Coast Survey Table : This table is superior to the above two types and is The levelling of the table is done very accllrately generally used for work of high precision. The table can be turned about the verucal axis with the help of the three foot screws. and can be fixed in any direction very accurately with the help of a clamp and tangent www.EasyEn. sdogttbttTostioIpdahdhbhrhceoteriteefnhoregireiyrvnsanaeoeshhiteweswdtwcsiuatthervitshiuaiienggihnaw.angensaakoos.c2lhehievsP.hlgnielsnriTeitnnnt.yyritesdlrasezeeTiTgtusaltlil.odliihiiAwamihbdescdnnronmn.aelisueeueoalinlolrgBetcsiytllaseidnnnwAhdeottuAoolieeshet,itanpttatpebsi.dslhdehcyhdsciileraj.ecldotspieloeoinxnIitnnmnoecnstntvtasighAooeasssatsAieftaile:gieittd.cmtfeitsoahldshhite.iticofeonasesdsAsvteadsTfoisrtnooedelret.nFhiismodritoebmotkmnsenhwsiyospenegfeiegeesAaulfd.eip.anftotnntstehrtrolhnmtathstfatesunjiriolhh(ieocoualdda1megFdure·aeilsbws1raihcrntiozemglart.htitdhela3o:ntesewnhrp.iaotnabiohnndlthegrcsalnalwseoet.(whelietas11urhenviarhn)lo1ottiataocoTairhhttopidnoc.iavealwgdsf4eahwiocPadslelsobenat.ie)eu.ix~elsdnlsiansauerntiinta·ctaosttgahsiisTisSh.danntolcpoeehttthielohohehpyrdtsnditarumTedneeeaeettaplahvchswifoeleaaosdaiehtaietrbsttfsnswdntihneenahuiirniimadmlwivaeelailtwtelteldieetsenoehhyclshielpeiotsneeJeacssleshliar·ivl,pneotwitttnkiDaragh.oaerpnataaeirhwewthetrtnngieeiwbiofpecagtodAleagoooeendeebooAhnorrodlvneffmktlat-efoaeds(vroh.tilfiioodvlhcnifiarcnlseentdtcsi)aatgegfnhaiacdrlauaaignmietke~nesgtgttnudlhe·hseitaeathaeeiedgh·besetdenstr('ltdpehee,lhki.tiedgatsepahwnfvisswuboaaeresitapcocaettsebpidthsssaotonewcreoehesoatuiiluadopiddhecncnurnntmlcsmiaheusehoctcteaisreellnsgdflepoawaiatotgtcnecrniumisthhanracmisaniaandtteofrluwcdineehntdioiorwtneirdrnduhcsoohteusfcpaa.ahleaaranefbgveadltodowi.clnlibeeshpc.ersenyiirTeedryohonnrrmo.idnhofTrtaemifittoikuevshdrshaebtlyaus,fiaireubreortedneedikphcstycsfa.eepwetaiepiohhnwdrcaooeebomfsgroOhlimtoriBielstjroxmtgitsaeroieqnenoesaevzkehcsinudJe'ahpyerdoa.dtpttlntum.aueininiguan•rtndsetoeoeotesoestaheeIgiatigossrded)ntfnn.ead.fl stadia arc may be provided. as an tx.ua. Thus. rht: observer can very quickly and easily obtain the true the plane table to a levelling .,.Point horizontal distance from and the diffemce in elevation otaff placed at the point between !hem. The same geomem\" principle apply to the alidade as to the transit, but the adjustments are somewhat modified in accordance with the lower degree of accuracy required. 3. Plumbing Fork : The plutnbing fork (Fig. work, is meant for centring 11.5), used in large scale or station occupied by the the table over the point plane table when the plotted position of that point is Also, in the beginning already known on •he sheet. transferring the ground of the work, it is meant for FIG. I L l Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net PLANB TABLB SURVEYING 273 point on to the sheet so that the plotted point and the ground station are in the same n vppiteittTaTtqttdanhshhoehwlostuiaheheesrericoaueneeepdmwrelcncctbrtaiitedoataoc.gthtrUsmcyiidobhlibpTihoao4Snb6cuplealetnSmw.hebh.cl.segurylesielioiltipneghdnanaysCtDSbahgeaendnaefwpesitsolrnog.adshaesialimdrlrinepratwrieotekwhecnvhgltisapusufteeitelithhasmrnnchlti·pieuche.tsaodtaLltgauodsehebrsennrraepmutne-ayTdasflbvPpnaht:il.lhwaroaselletmuaeyeetusettalbrTgiTemsdptldtpturrehmhhepashbil:taodeieteartiwetawaosrigvhfinanrvsmstAiheehtdhye:cgeptaaslhteoehbpuasnTomerfsltllschsmtreamlytlofhrphsamaihtapneinietaeelet·neintha.iee·aaeyrnhs·igsiteslrmhcdessdloabpFootaelrhdnanugeuipoaatdioniesrbndvetrblstwnarnpt-aumdlcebjisweiilititfledhnlruanndolrweetiinieoatssphgbtsestficdhepotmpsefsr-Oadeeebeecahrolnpckvbrideetoreantwtattyvnihbroftoprehooetboe.liptiuroeitthelprgtferarghfhhrspfelohlhaearootmutescohtlcuhnmftoarlgnihihdiesagdianingfpmhdeeaaydeusentghanpdnhcegttpt.gueebchtoliecfobtaeenebsoproehffqaTnlresesogumrten.uteoeheraltfiluaxpachbitruvyltnhrsnahpioaeephlsapseeemdsevaveelliosaeovnotedeehlsnnlbnasvrwoutapiecaeitriy,tenwsolonihiiobfraetdeoonnahmlhedntptfneraevyruiweotse-bbxaithtmaain.hhnarplhnaearioegtesedtioinnsmatshdcrcdshbgihgibcsi.eaatgellonryoooeorrelonmgmtiaadnfwtTtasruhsrituotaiuhdnsefreonotltiffasrhtdehetiifrtocnceireusmlttngufmohhaailfbmoylrialneecoeettptumtngeytgiaewrqilisrtorrfe,analcuslooknieierntgunlanmfsvbaat.tllioothpeeiacsadiodmslblrceovirlnoisudeaesfedpewnpenfnitdwplttttwheosyeygiiaoamrehorrtpbtewpethhirheinhoeeolteneetenee,ns,o,n..rsfrt gbacked with sheet aluminiutn are often used. inThree operations are needed (a) e(b) ering.nbatpFhnoooeairnrodtsrmtdaL(Cpitiocninle)oreoavenntrettytewlrpldoiioSnrnnseiggpgoc.p.ithinrhsotieeFitsTnitothghglirweeoervnosotemsuhrtslaknheab,dealmlle.te-ptaasoTcyrsiiachnghJlooetehohsrhutre.ewnoldssapouponersongkrhenal,deedt.iTsilonesanovTgbaelnheildeslptiolnaokgtgcarnteebhoitdsletwCeindnoogsoaivtsnsaaetttesrhiloeeSbncvtyhueebnerloveluterecsbidstcynbitumaglpetbTiaioyettahincdobeepnlneol.satprhrcilFaoamilnonutaghrelydienwttahhhogbbeeerrolkoetu.lheueonxsvfdAeaeddcsalit.rctlehycaocaulntrtrieooaacnvttdhhyseeye.,r et_dstpaihsoeroeesscriottrghidiorbaeobnOtepuesdernlniidruendet.snheesetunidsTatl.rtthiieinooipsIsgnnfre.i.sisod.neeOroanienercastienihnsentenagnotboiatvoytitheanaiorelanuriclcs.sl.e.oiinsrdFnntgaidtooshiirttnteoiaordoptndoirrponiiolrenteuceon,etctnostabibsfttoheiionnotehngffeu,toplafmnubfitolhtllatereeiptknhd..gwetaTwitblhhlphleeeleannnppowlrtamoiinlcshloeeer-sethpsapaeabtvsrahlaerealaolnleifltnleotclooenthnotesoetorimitninhrtgeossattetr2faliutfxnedmeddiadrerenocadtrdtbiiieiroosfenftunacettatlriiieoooointnnnnst 11.2. WORKING OPERATIONS Fixing : Fixing the table to the tripod. (iiz) Orientation. (I) Levelling the table (il) Centring Setting : Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 274 SURVEYING vertical axis, !hus disrurbing the centring. I f precise work requires that the plotted poinl should be exactly over the ground point, repeated orienllltion and table are necesmy. It has been shown in §11.9 that centriog is shifting of the whole a needless refinement www.afinavlalua((a((d(1ibac1bj))))u)lesOtOmrarWfnWWdeionejnurhhnhltwineeetlaclnnanTiitrotdhtonhsteinhepnemepbrebyeletidarygoanhatvierbtismeoslritueisbatngaebmegonhlieossgtrhscesrteooaeeoc.mafl·\\oit.!rpenlJabobraldppaensicigsdtlkp.hiotsoaraitaiTnnighenpthhnalptettorietnohradiacgxaveco.itanbmcmityulaaaapmtctbicaecoluoseunlsmaro,atrpfecbiotadeyyhrsn.ostueacogrtuorirhnoiomednrnpselleraltslsotsistinho. enbae.ccfcaourmlrrlyoaaiwtdnee,igngoptfrhtcieeoon.rnadptziotriimoovntuhestesh: for small-scale work. There are twO main methods of orienting the plane !able : (I) Orlenllltion by means of trough compass. E(rl) aFor orientation, the compass is so placed scentrally, and a fine pencil ystation, where the table is For approximate orientation prior to final adj}l'trnent (e) In certain resection problems. EnipcsltblGanihihoonnnerenideeepnedpalttiooslttaoiteistnhbo(tC(b(TrfTieeebatianyloiahd))l)ospsrsweneitergoawWaOeb.iWalbbhrdcymlarir(ltaihyehyeebskeene.i)mnbtnponthelpaoanweiospllsafatdoilisirhcntinlteiteoloedsitsossneniiiebnsdisdbrsonoscatietebhtc1ihfbpsedJraeotnrlyvoqaiteonoloneisauiaunrtndgbs!tiigaiaavieeatobtbbhhanppcnlwillleteronkeeeaetoihsrbtdtbhusfehsst.t(riiloehhiasboegdaemlm)nttThreo,enhgsaehttheeriw..lneotrtttwopthnonughgfrTeietn.saethtrdthtwadvofseaRbroOeiunoooeletrtnaeomsrpuhsiibidentneleseactanop,chniatnutsiltaellsacooisieltosentlotynatinsaetpiomeyphtoitrindtalenosepambnBvnanAlaaeiis,i.Aecvsony.snaceB,udnrlortsaseWataanbimapz·bc(rhbiuirsihadlpmaepsettetlesaehesrnutdoeeatditanooovnbho:xntntiepneihdinesbeodeietsnreAirtdnhra,ppooilevnidorndrseteehstoarhcipaesnlsittiearnlioihuestneociceecagnnhhldaediyl.iblni.enpyiyrdwvatea·rbaepcii§pyddntbtehilew,graoo1csnattitk1byiteghishy.sdheo6est.tfkihpaingoetpaeragnhpWlatrpottfnioetnlhtsttticihoheeghnimttennede.e).on the plane table that theneedle flpats line is ruled against the long side of the box. At any other to be oriented, the compass is placed against this line and floats centrally. The table is then clamped the table is oriented by rurning it until the needle ·.aTisissonhdettthrhaoeaanlnrStiisdefiagnetddhrhtrareeatetiwidnoilsgninntektofhherapeoosstmfuppcboscievtiiehgneoeehnttdseti.dnidnpgWosaantbsrhlesouie,enumnsettseho.tnoehntrecepsbptoialtsiothneiteotctsentsdtatobatllhlooeecbnaeghtsiaoisglntohncbeaoaletfeeendadthtgeseaetrhtie,neosfits.rpeiugto.hm,hienteetwndathtloeistdnhta.arbdotleieeuo.vgnpehllSlaoiinnttmthdgeeid,lia.scralelyAtirud,urarndirtneahedgye. · Downloaded From : www.EasyEngineering.net

PLANE TAIILB SURVEYING Downloaded From : www.EasyEngi2n7e5 ering.net ,III II rays to other points to be sighted are drawn. The points are finally plotted on the corresponding ;•Ij· rays either by way of intersection or by radistion as descn'bed in the following articles. )j 1obaaawwin1luuefiiis.ttdtt3oodehhat.-ldher.reee(vtaMPehidaldReub)tocuvicyEoadcettcsnCietiroeilFftlaoiJienedecmSnsndaiocSrspnlofet\"sveacpyeldctPea-asrliKi.ytnsLrseicd,aomAhlFssneouysNistrgsesai(iEltoznnsoe.oefgg1mfreTe1Tup.ngH.hAa7lCltealFaa,BnhsmidstegsaLeceamp.lrEm.tse.etawceeslwboereclhE-nln.roeFi6sQdcpetfhie.2rionUnacq2rngtsu)IecehPaSialopelMgnoiwxmdSirtavasEhtecbidaennNtaedettgheiTafsoeaiicrsrerreeirelpeeaodnedhnddqdnuot.ouiaoctnowitbefpIgigdyonprvnaeailavhdpaeidnaowhadierwnlsiiaocdztibiortoofohlefnefn(ws,it,uidat1hschli)tiaehhafggodvehtrciiatetasneu.ilmrlngestaeasisnsncbt(ccorgIoluo)eefpsmp,ipeeHcerwyaenaencaimta-tdsihlpsiimediseidtaetcelpidrelfe-reeafvFoespevecraplewnoilledoninpniaencteirghdcgels i c]l ~I 1.• ~ I :I nginasbceratedrwo, usiTgTshhh•aeerpecrpooblmvblaaiundpdieeaeltdsrsawibnwiflttoehoitrhisptmhacleraolaagclmnklpeeepilltdilcar·artuo,nlodertaihesaetsnatutlnallrelgcitvniehoegnmnltl.einensgaAtcsryehiswetuaobdppufreoolbrarvayritdieomesxnpdea.iacrnitwtsiotloherfiveeatmhl raceatieisrocnsuw.clareerAlwl ssp.apsilrTuimththebeleilnvetgevalenlgflaoiennrndkgt FIG. 11.7. FIELD OF VIEW (FENNEL'S AlJTO.REDUCI10N SYSTEM) 8 ee· rintwo serves precise centriog. METHODS (SYSTEMS) OF PLANE TABLING g.netdbtwthaiyshectheapnenploocoRImetTtmnhtiAheentitessDgtrhidcIimfstiAtoosootlelaTllmayonsbIsCwoOeuemtwerihNnesioeddgthdeat,srbaceietasalhtetlweeesdmrpe.astehyahnneTelhpitaseh(drweiesoditmrtfamhannewiesncttcehtenrelouesadssmsfocartoeorahynmppmatiescetsoatlsaaeatuhtnlliiroeogdwectnadhaidi.dt)neeaesEnrtardtvn(uhS.sidmedcetheoeeonappnnttoetlceyiphn,sqIaltssf_pait\\nthntietftgoeh,rrlnoeeamm2ntdi2eodnit)waShs.nttotarhadurnedimcnsiepssestontrhumitnaemlorcereapeinnsotoisnblcuostott,iacatnaiatntttibrheoeoldednel: Methods of plane rabling can be divided into four distinct heads while I. Radiation. 2. Intersection. 3. Traversing. 4. Resection. The jirsr two methods are generally employed for locating the derails the orlwr methods are used for locating the plane table stations. T (Fig 11.8) : Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 276 SURVEYING I . Set the table at T, level it and c E tranSfer the point on to the sheet by means ... , , ' ' of plumbing fork, thus getting point 1 rep- sight to A. Draw the ray along the fiducial ' '\", DI ,'/ ' ' ' ...... wedge of the alidade. Similarly, sight different :I / '/ resenting T. Clamp the table. ', I / ' \\...... / .2. Keep the alidade touching 1 and :I points B. C, wcorresponding wa~.:c···--····· ~the pin while sighting the points. . D, E etc., and draw the rays. A pin. may be i1Jserted etc., in the field and plot their distances .Eto some scale along the corresponding rays, thus getting a, b, c, d, e eiC. Join these at 1, and the alidade may be kepr·touching ]- · · b a .. aif needed. I - 3. M~ure TA, TB, TC, TD, TE s11.5. INTERSECTION f ----- ........... _,F yEnTsstaskhtttnnhaaaedottetiiiwooopnnnpnloosslIsocniiaitasttnt(tseioneptordoersntenoiheltvocehfoiocteooniaforiutnfnebsttttleahhayoraseneiossenepycosollrltohaibebinrptoejsjtgeeeeoeno.ecctdrrnttt).eoNtIot.dIofIraoSInTitsctdhlhodoiaienesemndetnweeiatdtoarwhrhriwtsneeostmmnricabneaneerefglcaoadtehyers.me!esulbribeTeeyadevfmhostiewresurresatmrytaeny@enelstsdin.cn,ejoetestiatThlstlhcheeghbjceenoeeurtitviarnwataett!wilhtDrneetaoetgeilhtneynxoeristntehdohthschoeuatfatebreitvuojaeet!mowpictofoteotaonritntifWfthatrinenolste)gmshta!atlabeenrestasudtieosmtnewhnteetwasrohlanvlioeiytfininsspecglsilDonatmwainnsSstttietehirtlioraluetmutnsmitgmuosaatirebdnwevenlesnideoes..tt (GRAPHIC TRIANGULATION) FIG. 11.8. RADIATION. rays ~ rY:'o sides and the base !me ~ c ~ the third lrne of the trtangJe. DUe to this reas9n. imersection is also someumes known ~ as gr_aphic triangulalion. ·----:0.:: \\ ''~ / \\_ Procedure (Fig. 11.9) : The fol- lowing is the procedure to locate the \\ '...... ,, pom, cs by the .method of m, tersect1, 0n: \\ .......... , ./, i {1) Set the table at A, level it and transfer the pom, t A on to the sheet by \\ \":( , /, ! way of plumbing fork. Clamp the table. I~ ,'I ' , '\"/.I, \\,\"\"\", ' :I compas(s2,) mWarikth !htehenohrettlrp diorefcttihoen otrnoutghhe 1: /1 / I ' ;.<I., \\,~,..' \\ :I sheet. l~ll]• II\\ /I /1 / ;' ' ' x ', '''~.. '\\ :1 _ (3) Pivoting the alidade about a, /I / I / I / / ' ' ' ' , , \"''~~' \\\\ I ~I\\ 1 I I1 , ._ \" \\ L 9 ab sigh• it 10 B. Measure AB and p!01 it A 8 FIG. I !.9. INTERSECfiON. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net PLANE TABLE SURVEYING m -'II i. along the ray to get b. The base line ab is thus drawn. and draw corresponding ' (4) Pivoting the alidade about a, sight the details C, D, E etc, ,J rays. 1' lI't~' (5) Shift tlie table at B and set it there. Orient the table roughly by compass and -I fcrcbfcaiaoonaoseyrrsanrseldegltslyhis<o.tipeXint(Too6G:bnahn)blctyereedi,yandnigpPngmbdhigwtava,haienccoatdkhytrepiaostonoryidfgtigeoishanthfencttoth.gtiahfnieuawlneogTnlithanenghbtigrtaliecAaseeolhse.irndestcphoaetwoeidccfosliteiainlnitilnoeineodnatbonegla;ersfl)eiissonsoeufuaoclottsmutfpefieoabdrlntoei,nhtcnhaceealeseyssosteipfgdaustoohhlustini!hwnerbdleedtsyaisetetdhhqrefeoaatuoohuryerreettsdnoetmmpttssharihacpoinuepaollrlstsalpeiueenmirlnedmsirgeonaacCtaynfpatd,rsopbye.tpelwteDdlaombTii,tlteshrstbetii.anaayEltsngteiIuhog.swfersneleeat,tm-cshytp.hitershaesnoehnvatfioni-sopuod4iuolnft5dsoitlnd'etyhrrtbbasieneeewsdchrbtusoaiwaouswtusheenclenleddh.l, :~ 11.6. TRAVERSING . ~ n dOwn ·a.psetatsatiarhaJetrectltie~itoaneebcndrso~.PtenobrtlcaHhyveTneatereIhmntnJoeeictetsadoaeaebmnb,sl-sleeepttrol•aattliirhlvrsn!aeeeitvfsr1tseshmeoSirwntsn'.aWeglhdyieai·icidnhstdevatflioononyfalfrovreeeutetrhsessioemngtsodtchehutewtectbhoepeisiesosa!ldiUmadniyttfethahesftekaea\"petri-wlenrieinwihndnticotcoiohptshrluetemwhrsIve·!ei!cal!ynalrsIfaJssoedsallliiau\"linoi'stbdtoerw-isasifoenwninnqbsrhutieahtietldewentirtatealrtafyiaevinatodnieronirbatnstheatheise_te.ohaunenAwscIdneamtoodssrteeebkriattsuihascenom5ohrgfdveloainstnpdtucrtisraaecoitsvtscnnritcueeocasrsmrnitisspiboiiaelenvenrnidegessst I• gof a closed or unclosed, traverse. iProcedure. (Fig.ll.IO) Ii'I' n(I} Set the table at A. Use c e -------------[,.Q]dplumbing fork for tranSferring A . •1!_ ........... 'l~ b on to the sheet. Draw the direction , , .... ·\"\".• a II C \\ er ~of magnetic meridian with the \\ II \\ ! help of trough compass. ! D ... ::>.:::~~· i(2) With the alidade pivoted ·-·- .•~.... nabout a, sight it to B and draw I . 8 _....- -!. .....g.... -.,.. [ ] \\the ray. Measure AB and scaleCP\",k·\"'\"\" .....\":.,. . 0'coff ab to some scale. Similarly, ! draw.....a. ray towards E, measure -.E•..i•.•·•·• ···-.. ,·-. DnAE and plot e. e(3) Shift the table to B tand set it. Orient the table ac- •., -. ea B curately by backsightingA. Clamp ·a ~ the -table. A (4) Pivoting the alidade about b, sight to C. Measure BC FIG. li.IO TRAVERSING. and plot it on the drawn . ray . Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 278 SURVEYING to the same scale. Similarly, the table can be se1 at other stations and the traverse is completed. tao(ornfe-tkhnn2eo)Iswttpsarttiaeistocthineoetdsonisnei.gnbrreoAasrttnacotoalitoonefnsydescdlshotaeastrrruteeairovenvethirstsaahietbo,lpuetohtgherhaetnioodttnhariebealonreefttarawttnivhooieelntlrshteiirnsaavvmettehoraestyoebseabbmmeedaeyoscnelseotbtsreoeabdniygcbhaeetbtvcalelcclinneekaed-ssbtigiywf(hintttishwn-egottt.Ihin)eogIsrftsatintatthiitoeoioonrrnense occupied. w11.7. RESECTION w'ITy whave been p/Qned. f!ffUPied of determining the pwned position of the sralion of which oj·slghls taken towardS kiiOwn poznts, locations .Eas·taotgghhtiifevveeetthshpseettlahaTthtesnihse!tbtaeanctatisroifoeomtrneqnraereutntciho·rdtitoeohddetlchobaeclcentoaoacptbnialoolbsoteiniiecnsoattnsshtoseaofdsooilnvfftheobkdedtnehnreeaonsbwtwthyaiientnonisorgttilnhmreou.enctamwtapeTtfo,ediohon.lentltrohaTwespaythr~smaeetbiingoltctorneeaar.mflyslot,eeshuIdcefrttdihortrtemhewansroweeeoitc.fnoh,ot)foopirbderoflsrt,sieho,nemtlsotiihesftsewotnhofoi~oenntkteernuncoerontsorsaiewperehcrcl_noeottnioctnottitrel.nnlsodygcoawotftlaioriobilcwelnla·enht'intiooceoahdnntt· Resection is the process· the pllliie table, ITy means y(!) Resection after orientation by compass. E(iz) n(iil) Resection after orientation by three\"j)Oint prob_lem. Resection after orientation by backsigbting. (lv) Resection after orientation by two-point _problem. ~--------·---------·-·······-···············-·~ {!) Resection after orientation by compass -. ',, / The method is utilised only for small-scale or / rough mapping for which the relatively large errors ',,, \\•yb'impair the usefulness of the map. due to orienting with the compass needle would not \\/ ',, / The method is as foilows (Fig. 11.11). (I) Let C be the instrument station to be located on the plan. Let A and B be two visible stations c which have been ploned on the sheet as a and b. 0 Set the table at C and orient i t with compass. Clamp I the table. FIG. 11.11. RESEcnON AFTER (2) Pivoting the alidade about a, draw a resector ORIENTATION BY COMPASS. (ray) towarda A ; similarly, sight B from b and draw give c, the required point. a resector. The intersection of the two resectors will (iz) Resection after orientation by backsightlng by backsighting along a previously ploned backsight line, the If the table can be oriented intersection of the backsight line and the resector drawn station can be located by the 1J \\l\\1#-\"' t retDowntlhoroaud.ge,hd~.F~1a7rn~o~om~t1h~~ea:cr:w~kA~wn~o•.wAw...AnE.l~a[ls.spy.-o~.Ein-.n.t-.gd(i\"Tno}hetlee,~r..»,i_m'n'ge\\t.•h\"n11oe1drtrA~Misr\"..,(;a\"(s-.f'o~lnlot-MwZfs.,(t~Fkig..~-~1-~1\".1~'27).-.. : j.v.'lll~\".}c./ t~.1 I ~ ~,..e<)·

Downloaded From : www.EasyEngin2e79ering.net li PLANl! TABLE SURVEYING II ~. • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . • . (I) Let C be the station to be \" located on the plan and A and B be _,.,.'' two visible poin!S which have been ploned J , ../ on the sheet as a and b. Set the table ,, / ,. at A and orient it by backsighting B _,.,·/ \\I along ab. A (2) Pivoting the alidade at·a, sight !ii EJ ..\\ C and draw a ray. Estimate roughly ..' .-t·~; \\ c,.the position of C on this ray as \\\\ .·,~;, \\ _,·' ii~ {3) Shift the table to C and centre ~'\\ ·'/ ' !ii it approximately with respect to c,. Keep \\ FIG. 11.12. c i!.~',!~ the alidade on the line c1 a and orient the table by back-sight to A. Clamp the RESEcnON AFTER ORIENTATION .BY i::' table which bas been oriented. BACKSIGIITING. (4) Pivoting the alidade about b, sight B and draw the . resector bB to intersect the ray c1 a in c. Thus, c is the location of the instrument station. ' Resection by Three-polnl Problem and Tw\"'polnl Problem n of either : first method is rarely used as the errors g (a) Three visible points and their ploned the second method, it is necessary to set ipositions (The three-point problem). due Of the two methods described above, the the ray towarda the station to be located. the to local table on attraction etc., are inevitable. In one of the known points and draw n(b) Two visible points and their plotted positions (The two-point problem). In the more usual case in which no such ray bas been drawn,.· the data must consist ,.;t···A<r:·········-·-···-···-·····-·-·········-·-···-·····-···-···;~ B \\ ell.ll. THE TIIREE-PO!NT PROBLEM // eStatement. LocoJjon of the position, \\\\ r Ion the plan, of the station occupied by \\\\ , / _/ ithe plane tabk ITy means of observalions \\\\ \\ / / ,/ \\ 1 nto three weU-defined points whose positions ghave been previously p/QUed on the plan. ' \\\\ / \\ '\\ ,/ i '.,~ ' ' i ., i .the table at the station with respect to three b i nvisible points already located on the plan. i i i p' i \\ l e./Let P (Fig. 11.13) be the instrument station tand A, B, C be the points which are located In other words, it is required to orient \"\\..' i. '/ \\i / '.i i ii,. as a. b, c respectively on the plan. The \"ic/ table. j:! said to be correctly oriented at P when the three resectors through a, b and F1G. 11.13. CONDmON Of CORRECT ORIENTATION Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 2aO SURVEYING c meet at a point aod not in a triangle. The intersection of the three resectors in a point gives the location of the instrumem station. Thus, in rhree-poinl problem, orienlalion and resecrion are accomplished in lhe some operalion. solution of the The following are some of the important methods available for the wPaper Method) problem :w(c) (a) Mechanical Method (Tracing 1. MECHANICAL METHOD ,(Tl\\ACING PAPER METHOD) wThe method involves the use -of, :('tracing paper aod is, therefore, also known as (b) Graphical Method rracing paper melhod. .Procedure (Fig. 11.14) ELet A, B. C be the known points and a, b, c be their plotted positions. Let aP be the position of the instrument station sto be located on the map. y(I) Set the table on P. Orient the table approximately with eye so that ab is Eparallel to AB. n(2) Fix a tracing paper on the sheet Lehmann's Method (Trial aod Error Method) oA ,s \\ -, i \\ i \\ ,/ '- ,./ \\ '-, \\ i ...........c. \\ \\ i '\\ ! ! a , w0./ ba' •C, ... ,.,/\" ..................... ,PI \"..., .e.... rt aod mark on it p' as the approximate location p' of P with the help of plumbing fork. FIG. IL14, (3) Pivoting the alidade at p', sight A, B, C in rum aod draw the corresponding lines p'a', p'b' aod p'c' on the tracing paper. These lines will not pass through a, b, aod c as the orientation is approximate. (4) Loose the tracing paper and rotate it on the drawing paper in such a way that the lines p'a', p'b' aod p'c' pass through a, b and c respectively. Transfer p' on to the sheer and represent it as p. Remove the tracing paper and join pa, pb and pc. (5) Keep the alidade on pa. The line of sight will not pass through A as- the oriemstion has not yet been corrected. To correct the oriemstion, loose the clamp aod rotate the plane table so that the line of sight passes through A. Clamp the table. The table is thus oriented. (6) To test the orientation, lreep the alidade along pb. I f the orientation is correct, the line of sight will pass through B. Similarly, the line of sight will pass through C when the alidade is kept on pc. 2. GRAPHICAL METHODS There are several graphical methods available, but the method given by Bessel is more suitable aod is described first Bessel's Graphical Solution (Fig. I 1.15) keep the alidade on b' a ·aod rotate the table (I) After having set the table at station P, so that A is bisected. Clamp the table. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 281 PLANE TABLE SURVEYING (2) Pivoting the alidade about b, sight to C and draw the ray x y along the edge ' of the alidade [Fig. 11.15 (a)]. (3) Keep the alidade along ab and rotate the table till B is bisected. Clamp the table. (4) Pivoting the alidade about a, sight to C. Draw the ray along the edge of the alidade to intersect the ray x y in c' [Fig. 11.15 (b)]. Join cc', ,A \\ \\ \\ \\ \\ \\ B• \\ \\ \\ ~'A\\ .i.oB c. \\ j \"'--- ~; ' l oA p u:•A (a) n ,a I•) ,.-c ,B ,l; nI I·~ 8 gineer ,.c i(b) / m ,.. c n/ ga, ,,'' / I• / ./ / n' 0 / etm p c lP (c) FIG, IUS. (c) : BESSEL'S FIG, 11.16 THRI!ll-PO!Nf PROBLEM Ml!THOD. Downloaded From : www.EasyEngineering.net

Downloaded From : www.EasyEngineering.net 282 SURVEYING Stitahfibemltehic.leairr((TclT65yuwh)h),meeoKPrfikepiftervaoeeobiapnintsllcietinsdetghaaidceoscetfahua,ceraliaiosdtbcemaa,i.lprdiccdiectvlael'ody.ateaelonHdondaregbinaeopcbnuceo!t',ecufdottbrh,mia[saFsniimdagagn.hedqttrhou1ottA1aaodd.t1er5iiBislsa.thtk(esecnDri)ago]rlthw.aatwbnealdne,datshtetiahl'llBelreaCstyrhsaeeyitlso'sfwobuiMiinslrlteeectprhptseooaedidscn.sttosCfcthllIacrineom' sucpgiarnhliobtnhpepegd. wQuadrilaleral'. wrays rays w.the done through a and b, and Eto be used for sighting and the asthe wdIrenarwetnhdertaofwiwrnsatrdtfhsoruotruhgeshtetphcs.i,r.dHthopewoiesnvitge,hr,·twinahgnicyhfortwisoortihpeneontianttissoingmhtaweydas in steps 5 and 6. spipgllaha(A(Wn12tnel))eilteBhSDrnitrmbaaaatabtwniiblldvaaelseeraldyticr,tGllaeliinlwnrdleatrrapAewtah,hCeieicsdcaipfirlbrseeaiptcsypSeetberocipnstlbteuehdeednecdlc.tdoeutinadoclCl.a.uilrdlacaam(CurtFdotlpeiatgom.aatthbepobe1ea1sittnhtia.ag1ebtah6le.te)ct..aBK[bFWKleeiega.ieptn.ehd.pt1'hidJbeh.re1aaaw6slaildic(dataheds)nede]t.ereraa,alyolondngibrgefcefatctot.haacnenuddtalrricoodfittlaadttienee yEn· IBothnr[oiFsutihggehb.((43is))ppe1lc.1JaTto.ne1oida6ns.thoe(eTrsbihoea)oJnnp.wtdocnshfite.thiceoiknUn tsatFiPhnbieglge.,ooafr1kisee1tehne.t1etpa6stqittoahu(nbeca,l)re.ea,dlroiddanrwsadwethreabayplsognrpogaeuArnp,pdeb.ncdCai,cnudlbaorrtohttoatoeeff.thwTehhicephnlanpsehoretuaplbdrleespeantsitlssl 3. LEHMANN'S METHOD in orienting the table at the is done by trial and error ...--,_ ,,. .paathnonedidnttaiesb,(PoWl\"eIcort)ceoharucpeSpherpmeiedarefotveudoxrerrhtieehmob.,aedylar.at(eetlRataslhydobeeylfseekortnsaaetobhFtewlaniegtnP..athbaIasan1nit1sdt.ht1tphhe7aioes)rratirletimlhnaerltleeteh-op•do'A',i..n.,'t,th',pe' ,r\\o'o.b..,rl..i.eemntaltiiIe/oIsn,, G...m.·a~:\\··.:lrc!e ...... / , .r. / / I :, ' ........ I •B \\ I\\ :to AB. Clamp the table. : : /I I I (2) Keep the alidade pivoted about ......... I I. \\ \\ , 1I I a and sight A. Draw the ray. Similarly, ..draw rays from b and c towards B and ...... .,·~ C respectively. If the orientation is correct, ~I the three rays will meet at one point If ' \\ ' ' {b- -p' p not, they will meet in three points forming Triangle one small triangle o f e\"or. of error (3) The triangle o f error so formed will give the idea for the further orientation. FIG. t l . l 7 . TRIANGLE OF ERROR METHOD. Downloaded From : www.EasyEngineering.net

PLANE TABLE SURVEYING Downloaded From : www.EasyEngin2e83ering.netl''·Ii' ;'! TTbTaoehothfeiswcddoohownrai((ci4ne5eiht)ld)hnl itwwsaKKs,gtiiiieteliogllveecinhepphbtoethwtonthCehsseie.leemxl thaaDetballhlila!erpdeeipadrswpadcprtodeohooefraxtirhanniemLeattc.l.tetoahbphrtnee'amogtynopaa.lorynspersn'iTvaie'gsiswhnohhethuoatasReswntenBiduontlr.neritaaarshonynTe(dtsgbahdluteeteedrwtsircaoaiantnlmwhplfbgepoeelraerrdtoeghrtxoaaeoibirlmanfa,lrcetaaecietmyfruert..rropeaoec'trethsShoiaigiiismtnschhetairblnoeaeAdnorel.uefnythc,eetCcthdrhklieaaoepmnestroeppgepnovlesitoo,hjitnutheuiedoesthinaceplitoiooadmobuisanelisade)ztly...eye il .I\\, ~ keeping in the view the W m • n n 's Rules. the ttiangle of error can be reduced to (6) Thus, by successive trial and error, a point. and correct position o f the table will be such thai the rays Aa. Bb and Cc The final mapSepeirmtoxiliTiTanmrhhleayeot,eulweitnhhfeeiosxsilanecjtgoiirolipcerntrlieonbpogplofeaiAmnsp.st,,'inBgstg.hoiuvtCshitn,rhogaui(tnogvtrhhtohelaevA,e,pstbori,Biana,nctg)pCfl.aefiororomrkfn(peao,rwrtolrbeir,adngcmge)laeyoiskf nbkoLenweohnwremndaausncanesthd'sethteGoRrGeuaalretesmaTtinrfoiCiamrinrugctmlhleee... Lehmann's Rules (1) I f the station P is outside also fall outside the great triangle and of error. Similarly, i f the station P is also be inside the great triangle and n of error (Fig. 11.18). the great ttiangle ABC: the triangle of error will gin• '('-.. the point p' should be chosen outside the triangle inside the great triangle, the triangle of error ·will the point p• shnuld be chosen inside the triangle · ee p~oi~nt;:.\"'~:t:~~lsnoutght~ rc Ore at biangle •b •-K-------/1-:::?/ )o inFIG. 11.18 ',, ~// g.netCirtacysshisoA(u(Ta23plh,d))roouTpTBagohbhlshre,eotiotpphnbooeaaeiinlnndatttbtoopopCv''cteth.hssehehrouourludTeillgisddhshtsatatbbnreeecoiesf,sssoouoBiffffbccilchxpPi>oaeonssnieedntfnnrtofmoCtthrhcpaatt'tAh(,FeiiitstisgBloicdschi1asao1tttnosia.od1ennn9ct)ehC.eotoffrrsopeatmsmh',peeectthhrtsiieevigdehefrltoyaly.looosfWf Aaitnalhlg.eFIG: I i.19 Bb, and the three ray Aa. sub-rules may also be useful : Downloaded From : www.EasyEngineering.net