UNIT 5 PLANE TABLE SURVEYING

Transcription

1 UNIT 5 PLANE TABLE SURVEYING Plne Tle Surveying Struture 5.1 Introdution Ojetives 5.2 Plne Tle Bsi Priniple Equipment Aessories Advntges nd Disdvntges 5.3 Setting Up the Plne Tle 5.4 Adjustments of Plne Tle 5.5 Reording Oservtions Rdition Intersetion Trversing 5.6 Resetion Simple Prolem (Bk Ry Method) Two-point Prolem Three-point Prolem 5.7 Errors in Plne Tling Fulty Instrument Adjustments Qulity of Drwing Pper Surveyor s Errors in Tle Setting Surveyor s Error in Oserving nd Plotting 5.8 Summry 5.9 Answers to SAQs 5.1 INTRODUCTION The plne tle is n instrument used for surveying y grphil method in whih the field work nd plotting re done simultneously. In plne tle surveying, n unknown point of interest is estlished y mesuring its diretions from known points. The min dvntge of plne tling is tht the topogrphi fetures to e mpped re in full view. Plne tle surveying is most suitle for smll nd medium sle mpping. Ojetives After studying this unit, you should e le to understnd the si priniple of plne tle surveying, its dvntges nd disdvntges, identify the equipment nd essories used in plne tling, desrie the djustments of plne tle, desrie the proedure of setting up the plne tle, 93

2 Elements of Survey understnd the proedures of reording oservtions, understnd vrious methods of resetion, nd desrie the possile errors in plne tling. 5.2 PLANE TABLE Bsi Priniple For quik nd pproximte surveying, when gret preision nd ury is not needed, plne tle surveying tehniques is very suitle. It is prtiulrly onvenient for filling the detils etween the sttions lredy fixed nd surveyed y more preise method of tringultion or theodolite trversing. For smll re surveys, plne tle is reommended. The gret dvntge of this tehnique is tht field work nd mp plotting is hieved simultneously y use of grphil surveying. The priniple used in plne tle surveying is tht n unknown point of interest n e estlished y mesuring its diretions from known points Equipment The plne tle essentilly onsists of simple drwing ord mounted on tripod similr to ompss or level. The drwing ord usully mde from well sesoned tek or pine wood. The size n vry from mm to mm. Sometimes squre ords of mm or mm re lso used ut size of squre ords is rther unommon. Another importnt onstituent of plne tle is stright edge lled Alidde. It is mde of metl (rss or gunmetl) or sesoned wood out 500 mm long with stright ruled edge whih is evelled. This edge is termed fiduil edge. It my e provided with sight vnes, t oth ends in plin lidde or (Figure 5.1) with telesope for etter ury s shown in Figures 5.1. In plin lidde one of the sight vnes is provided with nrrow slit nd the other is provided with ross nd stdi wires. Like level, two ule tues pled orthogonlly re provided for keeping the plne tle horizontl. The evelled edge is grduted so tht it n e used s sle for plotting distnes diretly on the mp. 94 Figure 5.1 nd : Equipment of Plne Tle

3 Plne Tle Surveying Aessories () Figure 5.1 : Plne Tle The dditionl equipment to e used for surveying with plne tle ould e s given elow : Trough Compss It is usully 15 m long, shown in Figure 5.2, nd is provided to plot the mgneti meridin (N-S diretion) to filitte orienttion of the plne tle in the mgneti meridin. Spirit Level Cirulr spirit level is used to hek the level of the ord nd mke it horizontl y pling it on the ord in two positions mutully t right ngles nd entering the ule in eh position. Pluming Fork It is lso known s U frme. It is hirpin shped rss frme hving two rms of equl length s depited in Figure 5.2. One end of the frme is pointed nd is kept over the drwing sheet touhing the plotted position of the instrument sttion. The other end of the frme rries plum o. The position of the plne tle is djusted until the plum o hngs over the sttion oupied y the instrument. Trough Compss Pluming Fork Figure 5.2 : Aessories 95

4 Elements of Survey Drwing Sheet Drwing pper should e of est qulity nd well sesoned to minimize the effet of limti vritions. The pper should e tinted green or grey for reduing glring in sun nd eye strins. Drwing pper is fixed on ord with drwing pins, lmps et. For drwing rys nd other detil qulity penils, dustless ruer nd preision sles re used. A wter-proof over is lso n essentil essories to protet drwing pper from dmpness nd rin Advntges nd Disdvntges Advntges Plne tle survey is most suitle for prepring smll-sle mps. It is most rpid. The field ook is not neessry s plotting is done in field onurrently with the field work, nd hene the mistkes in ooking the field notes re voided. () The surveyor n ompre the plotted work with the tul fetures of the re surveyed nd, thus, nnot overlook ny essentil fetures. (d) There is no possiility of omitting the neessry mesurements s the mp is plotted in the field. (e) Errors of mesurements nd plotting my e redily deteted y hek lines. (f) Contours nd irregulr ojets my e represented urtely, sine the trt is in view. (g) It is prtiulrly dvntgeous in mgneti re where ompss survey is not relile. (h) It is less ostly thn theodolite survey. (i) No gret skill is required to prepre stisftory mp. Disdvntges The plne tle is essentilly tropil instrument. It is not suitle for work in wet limte. It is hevy, umersome, nd wkwrd to rry. () There re severl essories to e rried nd, therefore, they re likely to e lost. (d) It is not intended for urte work. (e) If the survey is to e re-plotted to different sle or quntities re to e omputed, it is of gret inonveniene in sene of the field notes. 5.3 SETTING UP THE PLANE TABLE 96 The survey detils of ground fetures re normlly otined y sighting the ojet through sight vne or telesope of the lidde nd drwing rdil line. On this line the ojet sttion s distne is mrked to sle. The ojet s position on mp n lso e plotted y sighting the ojet from two different plne tle sttions nd loting the ojet y intersetion of rdil lines.

5 Sine survey is rried out y sighting, the tle should e set up to provide drwing ord t onvenient height out 1m ove ground. The tle shll lso e stle nd levelled. The legs of the tle re spred well prt to provide stility nd djusted to provide the tle in horizontl plne y mens of the levelling srews with referene to level tue. The tle is entered over the sttion urtely with the help of pluming fork or U frme. The upper leg of the fork oiniding with the point on pper while plum o is hung from the other leg diretly over the peg. The other essentil step in setting up the tle is its orienttion. It ensures tht the tle is kept prllel to its originl diretion s it is moved from sttion to sttion. This step is neessry to mke the lines on the mp prllel to the lines on the ground represented y them. This is hieved either y the use of ompss or y the proess of k sighting. Using the ompss, line is drwn on mp t first sttion in the diretion of mgneti meridin. Whenever the tle is required to e set up t new sttion, the ompss is pled in the diretion of lredy drwn mgneti meridin nd tle rotted to ring the needle ends on zero reding of sle. The tle lmped in this position ensures urte tle orienttion if no lol ttrtion is present t sttion. A more relile nd preferred method of orienttion is y k sighting. Whenever the tle is required to e shifted from instrument sttion O 1 to O 2, the O 2 is sighted y pling rnging rod t O 2 nd line of sight long O 1 O 2. A line O 1 O 2 is then drwn on mp. When the instrument is shifted to O 2, the lidde is kept long O 1 O 2 nd rnging rod pled t O 1 is sighted from O 2. The ord is rotted until the line of sight isets the rnging rod t O 1. Plne Tle Surveying 5.4 ADJUSTMENTS OF PLANE TABLE For plne tle survey to e dequte nd urte, following preutions shll e oserved nd djustment mde ordingly. The tle ord surfe shll e s perfetly plne s possile, otherwise the rys drwn on the drwing mp will experiene severl ostrutions nd hene will not e urte nd stright. The plneness of the ord n e heked y using the stright edge in severl diretions nd removing ridges nd higher spots y snd ppering. Plning n e undertken if roughness is ute. In ddition to eing plne nd smooth, the ord surfe should lso e horizontl, i.e. perpendiulr to the vertil xis of rottion of the tle. The horizontlity is heked y using the spirit level. The level is pled repetedly in perpendiulr positions nd ule heked for enter. Any devition from horizontlity is orreted using wsher/pking etween the ord nd the supports. The ule of the level shll remin entrl even when the tle is slowly revolved through 360 o. () In order to drw the rys in perfet stright lines, the ruling edge of the lidde shll e mintined stright. Any devitions shll e strightened y filing urtely. (d) The sight vnes provided on the lidde should e norml to the ruler se. This will ensure tht the line of sight of the instrument is prllel to the ruling edge so tht the rys drwn represent the diretion of the line of sight. 97

6 Elements of Survey (e) SAQ 1 This requirement n e tested y hnging plum line t distne from the instrument nd iset it with the sight vnes of the lidde. The error will e indited y hir line of vne tilting with respet to the plum line. Neessry djustment n e mde either y filling or pling some pking under the lidde se s required. The spirit level xes shll e prllel to the lidde se xes. Similr ury requirements nd djustment re neessry for telesopi lidde. Stte the dvntges nd disdvntges of plne tle surveying. In tht onditions would you reommend the doption of this method of surveying? Stte vrious djustments required to e rried out on plne tle. 5.5 RECORDING OBSERVATIONS One the tle is set nd oriented t ny instrument sttion, the detils of importnt ground fetures n e oserved nd reorded on mp. This is generlly rried out y three proedures nmely rdition, intersetion, nd trversing Rdition This is most diret nd simple method of reording oservtions during plne tle surveying. The instrument sttion O is seleted nd instrument is set nd oriented t this sttion. The point of interest, representing importnt ground fetures, nturl or reted, is loted on mp pln y drwing ry from the plne tle sttion to tht point with the help of lidde nd plotting to sle the mesured distne s shown in Figure 5.3. F E A e f d B D C Ground 98 Figure 5.3 : Rdil Lines Method

7 Smll lnd res n e surveyed from single instrument sttion on one tle setting t predetermined nd loted position. The instrument sttion is seleted suh tht entire re is visile nd pprohle from this position for distne mesuring nd sighting. The instrument sttion designted O 1 is plotted on drwing sheet extly oriented nd levelled t ground sttion O 1 with the help of U frme s depited in Figure 5.2. The vrious survey trget points A, B, C et. re sighted y entering the lidde on O 1 nd rys drwn long its edge. The distnes O 1 A, O 1 B et. n e mesured y hin/tpe nd plotted s O 1, O 1, on the sheet. The N-line is mrked t top of sheet with the help of ompss. This wy the trverse def n e plotted. Aury n e heked y mesuring ground distnes AB, BC et. nd ompring with mp distnes, et Intersetion In ple of one ground sttion O 1, s in rdil method, two ground sttions O 1 nd O 2 re seleted on ground, suh tht ll importnt fetures of re to e surveyed re sightle from oth sttions. The line joining instrument sttion O 1 nd O 2 is termed se line. It is the only distne whih is required to e mesured linerly on ground. With plne tle positioned t one sttion (sy O 1 ) the point is trnsferred on sheet s O 1 s in lst method. With lidde pivoted t O 1 different survey points A, B, C re sighted nd rdil lines O 1, O 1, O 1 re drwn. Next the plne tle is shifted nd positioned t O 2. With lidde pivoted t O 2, survey points A, B, C re sighted gin nd rdil line O 2 A, O 2 B, O 2 C re drwn on sheet. The intersetion of rdil lines, e.g. (O 1 nd O 2 ) will give the lotion of A on sheet s nd so on, without mking ny liner mesurement s shown in Figure 5.4. Plne Tle Surveying B A C o 1 o o 1 2 f e d f O 1 o 2 e d o 2 E F D Figure 5.4 : Method of Intersetion This method is generlly preferred for plotting the detils of ground, ojets, whih re fr wy or diffiult to ess, rivers et., nd the survey sttions whih n e susequently used s instrument sttions. It is prtiulrly useful in rough nd uneven regions where urte liner mesurements re tedious, or diffiult or even impossile in some ses. 99

8 Elements of Survey Trversing The method of rdils or intersetion (from se line O 1 O 2 ) n e used preferly for smll level surveys. However, plne tle n lso e used for trversing surveys of wide nd lrge res similr to hin nd ompss surveys, for oth losed nd open trversing. Survey lines O 1 O 2 O 3 n e run etween sttions whih re lredy predeided y other methods. The topogrphil detils re fixed y plne tle trversing. The step-y-step proedure n e desried s follows : Trverse sttions O 1, O 2..., O 3 re predeided on ground. Set nd level the tle t O 1 nd mrk o 1 on sheet extly ove O 1 using U frme. Centering the lidde t O 1, other trverse sttions O 2, O 3... et. whih n e sighted from O 1, re oserved nd rys O 1 O 2, O 1 O 3, O 1 O 4,..., et. re drwn. For topogrphil detils sttions A, B, C,..., et. re sighted nd rys drwn (Figure 5.4). () The tle is then shifted to next sttion O 2, fixed levelled nd oriented. Position of sttion O 2 is mrked on sheet. Rdil rys O 2 O 1, O 2 O 3, O 2 O 4 re then drwn with lidde entered on O 2. The intersetion of rys O 1 O 3 nd O 2 O 3 will give the lotion of sttion O 3 on sheet nd so on. The ground fetures A, B, C,... et. n e similrly loted on mp y drwing rys from sttion O 2. Detils n lso e loted y method of rdils. (d) The proess is ontinued till ompletion of survey. O 1 O 2 o 1 o2 o 1 o 2 o o 3 o 4 o 4 3 Chek Lines Chek Lines (e) O 4 o 1 o 2 o 4 o 3 o 1 o 2 o 3 o 4 Figure 5.5 : Trversing Aury is heked y sighting sttion O 1, O 2... et. from more thn two sttions so tht three rdil lines merge t referred sttion. However, if prtiulr trverse point is not oservle from more thn two trverse sttions, some well defined ojet on re n e temporrily hosen s instrument sttion for heking. O RESECTION 100 It is method of orienttion employed when the tle oupies position whih is not yet loted on the drwing sheet. Position of instrument sttion oupied y

9 the plne tle n e drwn on sheet (or mp) with the help of two or more well defined points whih re visile from instrument sttion nd whose positions hve lredy een drwn on pln mp Simple Prolem (Bk Ry Method) This method is very useful when one of the plotted sttions in essile from the sttion to e plotted. The proedure of resetion fter orienttion y k ry is given elow : Bse line O 1 O 2 is seleted on ground s distne etween two well defined points O 1 nd O 2 on ground whose positions re mesured nd plotted urtely on the pln mp. Set, level nd orient tle t O 1. Alidde is pled long O 1 O 2 suh tht signl t O 2 is iseted. With lidde t O 1 nother sttion O 3 is sighted, whih is required to e loted, drw line O 1 O 3, sttion O 3 is mrked on mp long this ry pproximtely. () Shift the tle nd set it fresh t O 3 nd orient it y ksight on O 1. (d) Ple lidde t O 2 on mp, sight O 2 on ground nd drw the ry O 2 O 3. The point of intersetion of rys O 1 O 3 nd O 2 O 3 will give or lote the position of O 3 on mp. This proess is repeted to otin positions of ll instrument sttions O 4, O 5... et. on mp Two-point Prolem The k ry method requires drwing the ry from preeding sttions (O 1 nd O 2 ) to the sttion to e oupied y plne tle (sy O 3 ). Errors of entering thus re inevitle. The two-point prolem onsists of loting the position of plne tle sttion on the drwing sheet y oservtion of two well defined points, whose positions hve lredy een plotted on pln. The proedure of resetion fter orienttion y two points is given elow. () (d) Let O 1 O 2 e the two sttions plotted s o 1 nd o 2 on the drwing sheet. It is required to plot sttion O 3 for plne tling work. An uxiliry point A on ground is seleted suh tht AO 3 is pproximtely prllel to O 1 O 2 nd the ngle O 3 O 1 A nd O 3 O 2 A re lned ngles, i.e. these re neither too ute or too otuse. The tle is set nd levelled t A, nd so oriented tht line O 1 O 2 on ground is nerly prllel to line o 1 o 2 plotted on tle mp. Alidde, touhing o 2 nd sighting O 2 on ground, ry is drwn through o 2. In the sme wy, drw ry y touhing lidde to o 1 nd sighting O 1 on ground. This ry will interset the first ry t 1 on the mp. With lidde touhing 1, sight O 3 nd drw the ry 1 o 3. Mrk the estimted position of O 3 on the mp s o 3. (e) The tle is removed from A nd set t O 3 with mrked position of o 3 over O 3, properly levelled nd similrly oriented. This is hieved y k sighting A from O 3. (f) Now with tle t O 3, keep lidde touhing o 1 nd sight O 1 nd drw k ry reseting the line 1 o 3 in o 3. Here o 3 is the point Plne Tle Surveying 101

10 Elements of Survey (g) representing the sttion O 3 with referene to the pproximte orienttion mde t A. With lidde touhing o 3, sight O 2 nd drw ry to O 2. If the ry psses through the plotted point o 2, the orienttion of the tle is orret nd o 3 is the orret position of O 3. Wheres, if this ry uts the previously plotted line 1 o 2 t some other point, sy o 2, then the position o 3 is not the orret position of O 3. O 1 O 2 o 2 o1o is Orienttion Error 2 ' o 1 o2 o 1 o' o2 2 B 1 A o 3 ' 1 o 3 O 3 Rottion of Tle t O Figure 5.6 : Two-point Prolem (h) The orienttion error will e equl to o2 o1o2 etween the lines o 1 o 2 nd o 1 o 2. This error n e eliminted y rotting the tle through the ngle o 2 o 1 o 2. This tle rottion n e hieved y tking the following steps. (i) (ii) The lidde is pled long line o 1 o 2 nd rnging rod B is fixed in line with o 1 o 2, fr wy from the plne tle. Alidde is now kept long true line o 1 o 2 nd tle is rotted so tht rnging rod B is iseted. The tle is lmped in new position. (iii) The true lotion of O 3 on mp is now mrked y : orienting lidde long o 1 O 1 nd drwing the ry o 1 O 1, nd orienting lidde long o 2 O 2 nd drwing the ry o 2 O 2. The point of intersetion of the two rys will give the orret position of O 3 (the new tle position) on mp. The new position of tle sttion O 3 is, thus, orretly mrked on mp with the help of two previous tle sttions O 1 nd O 2 lredy mrked on mp. The proedure followed is termed two-point prolem in plne tle survey Three-point Prolem The position of new plne tle sttion on the mp n e orretly loted with the help of three well defined points on ground whose positions re lredy plotted on mp. Suh proedure is lled three-point prolem. It is ovious tht loting the position of tle y this proess is more urte. However, it is more involved nd omplex.

11 Let there re three ground sttions A, B nd C whose positions re mrked s, nd on the pln mp nd let these sttions re visile from new tle sttion O. It is required to plot the position of O on mp s o. This n e hieved y ny of the following methods : () Mehnil Grphil Tril nd Error Mehnil or Tring Pper Method The proess of mehnil method is pplied using tring pper or loth. The tle is sttioned, set nd levelled t sttion O nd is oriented s nerly s possile in its orret position either y visul judgment or y use of ompss. A tring loth/pper is spred nd strethed over the tle. The position of O is guesstimted nd fixed on the tring to pproximtely lote the tle sttion O on the mp s o. With lidde entered t o, sttions A, B nd C re iseted nd rys o, o nd o re drwn on the tring. The tring is then un-strethed nd rotted until the three new drwn rys pss through plotted positions of, nd on the mp. This will provide new position of sttion O on mp s o. This is trnsferred to mp y pin of fine needle point. The lidde is then pled long o nd sttion A is iseted y rotting the tle nd then lmping it in new position. Sttions B nd C re then sighted nd rys drwn s hek. The new rys shll pss through o if new tle orienttion is orret. However, smll tringle of error my e formed s tle orienttion ws only pproximte. The ove proess is then repeted y tril nd error till the tringle of error vnishes. Plne Tle Surveying A B C A B C o o' Figure 5.7 : Mehnil or Tring Pper Method Grphil Method Severl grphil methods re suggested to solve the three-point prolem. However, the Bessel s solution is the most ommonly used method in prtie eing the simplest. The Bessel s solution n e desried in the following steps : The plne tle is set up nd levelled t new sttion O. The lidde is pled long known line (sy on the mp) nd tle is rotted until A is sighted with pointing towrds A s shown in Figure 5.8, lmp the tle nd sight C with lidde entered on, drw line x-x long lidde edge. The lidde is now pled long nd tle turned to iset B with towrds B s in Figure 5.8. Clmp the tle nd entre the lidde t, iset C y drwing the ry C interseting the previously drwn ry x-x t point (sy). Join. 103

12 Elements of Survey () Alidde is now pled long s in Figure 5.8() nd tle turned till C is iseted nd lmped in new position. The tle is orretly oriented. (d) The lidde is entered t nd B is iseted. Drw the ry to interset in o. Similrly, if lidde is pivoted out nd A is sighted, the ry will pss through o if the proess is urte. Any minor error is orreted ordingly. A B C x x O B C x x O A B C x O o x 104 () Figure 5.8 : Grphil Method

13 Tril nd Error Method or Lehmnn s Method Plne Tle Surveying This method is very ommonly used in field nd is quite quik nd very urte. The plne tle is sttioned, set nd levelled t sttion O nd is oriented s nerly s possile into orret position either y visul judgment or y use of ompss. Rys A, B nd C through plotted points, nd re drwn sighting sttions A, B nd C long A, B nd C respetively. If the tle ws oriented orretly to strt with, ll these rys will interset t ommon point o on the mp inditing orret position of sttion O. However, sine the initil orienttion ws only pproximte, smll tringle o 1 o 2 o 3 will e formed in ple of ommon point o. This tringle is lled tringle of error nd is shown in Figure 5.9. This tringle is ttempted to shrink to point y tril nd error, so tht in finl positions lines A, B nd C pss through single point o. The proess pplied to hieve this ojet is known s Lehmnn s rule. The tringle formed y joining sttions A, B nd C is termed gret tringle while the irle pssing through A, B nd C s gret irle (Figure 5.9). B Gret Cirle Gret Tringle o 2 o 1 o 3 A C Tringle of Error t o o Tringle of Error () (d) e o (e) Figure 5.9 : Lehmnn s Rule 105

14 Elements of Survey Lehmnn s Rule The Lehmnn s rule n e stted s follow : The distne of true position of o from eh of ry A, B nd C is proportionl to the distne of O from ground sttions A, B nd C respetively. If we look in the diretions of sttions A, B or C, the true position of sttion O is on the sme side of the three rys A, B or C, i.e. if the tle sttion O is outside the gret tringle ABC, the tringle of error will e outside the tringle nd o will e outside of. Similrly, if tle sttion O is within the tringle ABC, the tringle of error will e inside nd o will e inside the tringle of error. () If the tle sttion O is outside the gret tringle ut inside the gret irle, the ry to middle sttion B, B in Figure 5.9(d) lies etween the true sttion position o nd intersetion of other two rys (i.e. A nd C). (d) When tle sttion is outside the gret irle, the tle position O in Figure 5.9(e) is on the sme side of ry towrds most distnt point (A) s the intersetion of other two rys, e. Using ove rules, the tringle of error is sought to e shrunk to point quikly. The first tringle of error is used to lote new tril position of O (sy o 1 ) nd pling lidde long o 1 nd the one of the known point (sy ) nd then rotting the tle so tht A is sighted. Clmping the tle in new position, B nd C re sighted nd rys drwn. The new tringle of error is generted whih is muh smller thn the first tringle of error. New position of tle sttion (sy o 2 ) is mrked using Lehmnn s rules. The proess is repeted until ll the rys A, B nd C interset t single point o. SAQ 2 Explin in detil with the help of skethes how you would urtely orient the instrument t sttion using two-point prolem tehnique. Explin lerly the three-point prolem nd desrie vrious methods of its solution. Whih method will you dopt in your se nd why? 5.7 ERRORS IN PLANE TABLING 106 The min soures of errors in plne tle survey n e rodly lssified s follows : Due to fulty instrument djustments Due to qulity of drwing pper used in mp plotting

15 () (d) Humn errors of surveyor in entering nd orienting the tle Surveyor s error in oserving nd plotting Fulty Instrument Adjustments The instrument, if not properly djusted, will introdue mny errors in plne tle survey. These djustments, whih re normlly required, their methods of testing nd susequently orreting re desried in detil in Setion Qulity of Drwing Pper The drwing pper strethed on the plne tle ord for reording the survey detils nd plotting the pln shll e of good qulity. The expnsion, ontrtion nd shrinking of pper due to temperture nd moisture hnges n use errors in survey mp reding even if it is prepred error free. The errors due to these n e minimized y using the plotted sle Surveyor s Errors in Tle Setting There n e primrily two types of errors whih re : Inurte Centering inurte entering of tle, nd inurte orienttion of tle. The position of instrumenttion sttion on mp shll e extly over the sttion on ground it represents. The importne of urte entering n e est emphsized y explining the nture nd impt of error on survey ury. Let O G e the instrument sttion over whih the instrument is required to e set up nd O P its plotted position on mp pln s shown in Figure AO G B is the desired ngle to e plotted, while AO P B is orresponding ngle otined y drwing rys AO P nd BO P with lidde entered t O P. Plne Tle Surveying A B β α 1 O 1 P 2 2 O G Figure 5.10 : Effet of Inurte Centering The ngulr differene ( AO G B AO P B) represents the error introdued due to inurte entering. The mgnitude of error will e inversely proportionl to the distne of referene sttions A nd B from instrument sttion O G. Insted of O G nd O P eing oinident, n ngle α (= O G AO P ) is introdued nd hene similrity n ngle β (= Ο G BO P ) for sttion 107

16 Elements of Survey B. Let us lso drw perpendiulrs from O G on ry O P B t 2 nd on ry O P A t 2. It n then e oserved tht sin α = OG2 O A G or, α= sin O O A 1 G 2 OG2 nd sinβ= O B or, β= sin G G O O B 1 G 2 G The ngulr error ΑΟ G B ΑΟ P B would e equl to α + β. It n lso e oserved tht the position of A on the mp mrked s 1 is not urte. It will e some position on the mp left of 1. Similrly, the true position of B on the mp represented y will e on the right of plotted position 1. The devitions of positions of A nd B would e 1 = α 1 2 nd 1 = β 1 2 respetively. These errors will depend on the sle of mp hosen. Thus, if sle hosen is 1 m on sle = n meters on ground, the A OG plotted length O P 1 = m n nd O p 1 = BO G n ms. AO Atul distne 1 = G α m = e1 (sy), nd n BO nd 1 = G β m = e (sy). 2 n Usully, during ploting, the mximum ury of plotting whih n e hieved y even n experiened surveyor ould e ¼ of millimeter, i.e. (1/40) m; hene devition 1 or 1 whih ould use error in plotting would e notiele only when it is equl to or more thn (1/40) m. Thus, minimum vlue of n e to e notied will e 1/ or e= n 40 In other words, e must not exeed n/40. It n lso e oserved tht norml size of the plne tle is suh tht mximum re on drwing sheet used for plotting ould e 100 m 60 m. Hene, in generl, the perpendiulrs OB G 2 nd O G 2 nnot exeed 50 m in x-diretion nd 30 m in y-diretion. From this, tle n e prepred for different length of sights to get n ide of ngulr error whih n e introdued due to inurte entering.

17 Length of Sight (m) Length of O G 2 or O G 2 (m) Vlue of α or β Angulr Error α + β o o o o o o o o o o From the oservtions mde ove, it n e seen tht if smller lnd re is eing surveyed nd plotted with sle ftor n of smller mgnitude, the error due to inurte entering of tle will e more ritil, the importne ftor grdully deresing with lrger nd lrger vlues of n. Inurte Orienttion When the tle is set t new instrument sttion, the orret orienttion is rther more importnt thn orret entering. The position of instrument sttion should e urtely orresponding to its plotted position on the mp. The survey detils lredy plotted on the mp from previous instrument sttions n synhronize with detils to e plotted on mp from new instrument sttion only when the plne tle is urtely entered nd oriented in new position. The orret orienttion n e hieved y heking the orienttion y two-point or three-point prolem s desried in Setions nd Preferly the orienttion of the tle should e heked from s mny sttions s possile y sighting two distnt nd prominent referene sttions whih re lredy plotted on the mp, therey eliminting the tringle of errors. The orienttion of tle shll lso e heked fter oservtions, preferly fter reording eh oservtion to eliminte ny hne rottion of tle during the oservtion proess due to improper lmping of tle Surveyor s Error in Oserving nd Plotting Humn error n e introdued during oservtion nd plotting of detils y the surveyor. These ould e due to ojets not eing sighted nd iseted in sight vnes urtely, the entering of lidde on the desired sttion point on pper my not e urte, the rditing ry towrds the desired ojet my not e orretly drwn through the referred sttion point, nd plotting of detils my not e properly done or reorded. Cre should e exerised during oservtion proess to eliminte these types of errors. Rndom reheking of some detils reorded t referred instrument sttion is desirle. Plne Tle Surveying Exmple 5.1 A plne tle is set up t instrument sttion O nd entered. After reording the detils of ojet point A, it ws oserved tht point O P, the plotted position of sttion O is not extly ove ground position of O. 109

18 Elements of Survey Solution It is oserved tht displement of O norml to ry O P A is 21 ms. Find the onsequent displement of the plotted position of A from its true position with referene to following dt : Sle of the pln 1 m = 100 m Atul ground distne OA = 3000 m Also lulte the sme if OA = 10 m nd sle is 1 m = 1 m. Distne O P = 3000 m 100 Error in diretion 0.21 α= rdins 3000 Displement of from its true position Angulr error = = ms o =α+β= 2 sin = O O Displement of from true position Angulr error = o =α+β= 2 sin = = 0.21 m SAQ 3 Wht re the vrious soures of error in plne tle surveying? How these n e eliminted in rel life projets? 5.8 SUMMARY Plne tle is most suitle for the filling in of the detils etween the sttions previously fixed y tringultion or theodolite trversing. The plne tle onsists essentilly of drwing ord nd lidde. Trough ompss, pluming fork, spirit level nd drwing sheet re the essories tht re required in plne tle survey. Proper entering nd orienttion of plne tle re the two importnt opertions tht re neessry to get ury in plne tle survey work. Inurte entering nd orienttion of tle will led to erroneous survey work. 5.9 ANSWERS TO SAQs 110 Refer the relevnt preeding text in the unit or other useful ooks on the topi listed in the setion Further Reding given t the end to get the nswers of the SAQs.