skp engineering college -...

Civil Engineering Department

SKP Engineering College

Tiruvannamalai

Department of Civil Engineering


Tiruvannamalai

55 Surveying I


Tiruvannamalai – 606611

A Course Material

on

Surveying I

BY

SANKAR.S

Assistant Professor

Department of Civil Engineering


Tiruvannamalai -606611

Surveying I

S.K.P. Engineering College, Tiruvannamalai V SEM

Civil Engineering Department 2 surveying I

Quality Certificate

This is to Certify that the Electronic Study Material

Subject Code: CE 6404

Subject Name: SURVEYING I

Year/Sem: II / III

Being prepared by me and it meets the knowledge requirement of the University curriculum.

Signature of the Author

Name: .Sankar.S

Designation: Assistant Professor

This is to certify that the course material being prepared by Mr.S.Sankar is of the adequate quality. He

has referred more than five books and one among them is from abroad author.

Signature of HD Signature of the Principal

Name: A.Saravanan Name: Dr.V.Subramania Bharathi

Seal: Seal:



CE6304 SURVEYING I L T

P C

OBJECTIVES:

To introduce the principles of various surveying methods and applications

to Civil

UNIT I FUNDAMENTALS AND CHAIN SURVEYING 9

Definition- Classifications - Basic principles-Equipment and accessories for

ranging and chaining – Methods of ranging - well conditioned triangles – Errors in

linear measurement and their corrections - Obstacles - Traversing – Plotting –

applications- enlarging the reducing the figures – Areas enclosed by straight line

irregular figures- digital planimetre.

UNIT II COMPASS AND PLANE TABLE SURVEYING 9

Compass – Basic principles - Types - Bearing - Systems and conversions- Sources

of errors- Local attraction - Magnetic declination-Dip-Traversing - Plotting -

Adjustment of closing error – applications - Plane table and its accessories -

Merits and demerits - Radiation - Intersection - Resection – Traversing- sources of errors

– applications.

UNITIII LEVELLING 9

Level line - Horizontal line - Datum - Bench marks -Levels and staves -

temporary and permanent adjustments – Methods of levelling - Fly levelling - Check

levelling - Procedure in levelling - Booking -Reduction - Curvature and refraction -



Reciprocal levelling – Sources ofErrors in levelling- Precise levelling - Types of

instruments - Adjustments - Field procedure

UNIT IV LEVELLING APPLICATIONS 9

Longitudinal and Cross-section-Plotting - Contouring - Methods - Characteristics and uses

of contours – Plotting – Methods of interpolating contours – Computations of cross

sectional areas and volumes - Earthwork calculations - Capacity of reservoirs - Mass

haul diagrams.

UNIT V THEODOLITE SURVEYING

Theodolite - Types - Description - Horizontal and vertical angles - Temporary and

permanent adjustments – Heights and distances– Tangential and Stadia

Tacheometry – Subtense method.

.



CONTENTS

S.No Particulars Page

1 Unit – I 2

2 Unit – II 52

3 Unit – III 69

4 Unit – IV 111

5 Unit – V 121



UNIT-I

INTRODUCTION AND CHAIN SURVEYING

PART-A

1. Describe the principle of surveying. (CO1-L1-AUC Apr/May2011) (AUC

Nov/Dec2011)

Thefundamental principles upon which thesurveyingisbeing carriedoutare

�Working from whole to part.

� After deciding the position of anypoint, itsreference must bekeptfrom at least two

permanentobjectsor stationswhose positionshave alreadybeenwell defined.

2. What is the purpose of an optical square? (CO1-L1-AUC Apr/May2011

Itismoreaccuratethanthecrossstaffanditcanbeusedforlocatingobjectssituatedatlarger

distances. Itissmall and compact handinstrumentandworksontheprinciple ofreflection.

3. Give the conventional signs for BenchMark and Cultivated land. (AUCApr/May2010)

4. What do you mean by reciprocal ranging?

(AUCApr/May2010)



When theendstationsarenotintervisibleduetohigh groundora hilloriftheendsaretoo

long.Insuchcases,intermediatepointscanbe fixedonthesurveylineby aprocessknownas

Reciprocal rangingor Indirect ranging.

5. What do you mean by scalein surveying? (CO1-L1-AUC Nov/Dec2011)

Scaleisa fixed ratio thatevery distanceontheplanbearswithcorrespondingdistanceon the

ground. For example:1cm =10m.

6. Define and distinguish between plane and geodetic surveying. (CO1-L1-AUC Nov/Dec2011)

S.No Plane Surveying Geodetic Surveying

1

It isa processofsurveyingin which the

portionof theearthbeing

surveyedis consideredaplane.

It isa processofsurveyingin which theshape

and size oftheearthareconsidered.

2

Surveysforthelocationand

constructionofhighwaysandroads,

canals,landingfields, and

railroadsare classifiedunder plane

Thepositionsare expressedas latitudes(angles

northorsouthofthe Equator)andlongitudes

(angles eastorwestofaprimemeridian)oras

3

Inthistraining manual,we will discuss

primarilythemethods usedin

plane surveyingrather thanthose

Themethods usedingeodetic surveyingare

beyondthescopeofthistrainingmanual.



7. Define conditioned triangles.(AUC Nov/Dec2010)

Theaccuracy ofatriangulationsystem,inwhichany errorinangular measurementhas a

minimumeffectuponthecomputedlengths, isknown aswell-conditionedtriangle.

8. Explain the range of reciprocal ranging. (CO1-L1-AUC

May/June 2013)

The vision rangingand line rangercan be adopted onlywhen the end stations are inter-

visible.Thelineofsightbetween twostationsisobstructedby naturalorman-madeobjectsornot

clearlyvisible.Undersuch conditions, indirect orreciprocal rangingisapplicable.

9. What do you mean by plane surveying? (CO1-L1-AUC May/June 2013)

Plane surveyingisa process ofsurveyinginwhich the portion ofthe earth beingsurveyed is

consideredaplane. In thistrainingmanual,weusedinplanesurveyingratherthan those usedin

geodeticsurveying.

10.What is meant by geodetic surveying?(AUC Nov/Dec2012)

Geodetic surveyingis a process ofsurveyingin which the shape and sizeofthe earth are

considered.Themethodsused ingeodeticsurveyingarebeyondthescopeofthis trainingmanual.

11.What do you require indirect ranging? (CO1-L1-AUC Nov/Dec2012)

TwointermediatepointsC1 andD1 areselectedwhicharenotalongthelineofsightAB

(surveyline).StationsC1 andD1 areapproximatelyinlinesuchthatlineC1 D1 isapproximately

paralleled toAB.C1issosituated thatbothD1andB arevisible fromit,while fromD1bothA andC1

canbesighted.

12.Name thedifferent methods adoptedin scale of aplan/map.( CO1-L1-AUC May/June

2012)



�Plain Scale

�Diagonal Scale

�VernierScale

�Scale ofchords

13.What are arrows? (CO1-L1-AUC

Nov/Dec2009)

Arrowsarealsocalledmarkingorchainingpins,andare used to markthe endofeach chain

during theprocessof chaining.

14.What is plumbBob? (CO1-L1-AUC Nov/Dec2009)

PlumbBobisusedtolocatepointsdirectlybelow oraboveanotherpoint.Itisalsousedfor

accurately centeringofcompassorlevelortheodoliteoverastationmark,and fortestingthe

verticalityofrangingpoles.

15.Define surveying.

Surveyingisdefinedasthescienceofmakingmeasurementsoftheearthspecifically the

surfaceof theearth.

16.Wha tare the works of a surveyor in office?

Inofficework,convertingfieldmeasurements(alsocalledreducing)involvestheprocess of

computing,adjusting,and applyinga standardrule tonumerical values.

17.What are the types of corrections to beapplied?

�CorrectionforLength.



�Correctionfor Temperature.

�CorrectionforPull.

�CorrectionforSag.

�CorrectionforSlope.



18.What are the instruments usedinchainsurveying?

a)Instrumentsused for measuringdistances

�Chain

�Tape

b)Instrumentsused for markingsurveystations

�Ranging rod

�Offset rod

�Laths andwhites

�Pegs

c)Instrumentsusedforsettingrightangles

�Cross staff

�Optical square

d)Otherinstruments:

�Arrow

�Plumbbob

19.What are the different types of errors inlinear measurement?

a) Instrumental errors

b) Observational

errors



�GrossErrors

�SystematicErrors

�Accidentalorrandomerrors

20.What is meant by direct ranging?

Whenintermediaterangingrodsarefixedonastraightlinebydirectobservationfromend

stations, theprocess isknown asDirectranging.

21.What are the conventional signs used to denote the following.

(i) Road(ii) railwaysingleline (iii) railwaydoubleline(iv)bridge(v)pond and stream

(vi)church(vii)canal lock (viii) chain

line.

S.No Description Symbol

1 Road

2 Railwaysingleline

3

Railwaydoubleline

4

Bridge



1. Write short noteson

a) AnEngineerschain.

PART-B (16marks)

b) Crossstaff. (CO1-H1-

AUCApr/May2011)

a)An Engineerschain:

Itis100ftlongor 20m lengthandit isdivided into 100links. Eachlinkis1ftin a length.

Usedin allEngineeringsurveys.Thedistances measuredwith theengineer’s chain

arerecordedin feet and decimals.

To enablethereadingof fractionsofachain withoutmuchdifficulty,tallies arefixedat every

five-meter lengthandsmall brassringsare providedat everymeterlength, exceptwhere tallies

are attached.Connectinglinksbetween two large linksareoval in shape, thecentral

onebeinga circular ring. Thelengthofthechainismarkedover thehandleto

indicatethelengthand alsoto distinguishfrom non-metallicchains. Thelengthofeachlink is

0.2m (20cm) in 20m chain is provided with100 links and30mchaindivided into150links.

Thistypeofchain is used incountries where FPS systemisstill used.

Theadvantagesof thechain are

�Itisverysuitablefor roughusage

�It canbeeasilyrepairedin thefield and



�It canbeeasilyread.



b)CrossStaff:

MadeofBrass/AluminumcomesinwoodencarryingboxandwithPole.Size100mm&



150mm available.

Cross-staffisused for(i)findingthe footoftheperpendicularfromagivenpointtoaline,

and(ii)settingoutarightangleatagivenpointonaline.Therearetwotypesofcross-staff,

namely,(1)theopenand (2) theFrench,thefirst one beingincommonuse.

Open cross-staff:

Thesimplest formofcross staffis theopencrossstaff.Itconsists oftwoparts (1)thehead

and(2)theleg.Theheadconsistsof four metal armswithverticalslits.Thearmsarerigidly fixedin

suchamannersothatthecenterofonepairofarms formingastraightlinemakesrightanglewith

theotherpairofarms.Inoneline,oneoftheslits isnarrowerthan the other.Onehorsehairisfixed

atthecenterofthewiderslit.Theobjectissightedfromthenarrowslitinlinewiththehair.The

crossstaffismountedon25mmdiameter,about1.5metrelongpoleforfixingontheground (Fig.7).



Forlayingoutarightangleatapointonthechainline,thecrossstaffisheldvertically on

thesupportingpoleatthe givenpoint.Rangingrodis fixedonthechain lineoneithersideofthe cross

staffandsighted through theslitandhorse hair. The crossstaffis turned tilltherangingrod is

visible.Atthistime,onesightthroughtheotherpairofslitsandanotherpersonfixesarangingrod

inthislineofsight.Footofthecrossstaffjoinedwiththerangingrodgivesperpendicularlinewith

thechain line.

2. Give A list of sources Of error in chainsurveyand Say which of the are cumulative And

Whicharecompensating? (CO1-H1-AUC May/June 2012)( CO1-

H1-AUCApr/May2011) Errorsin Chaining:

a) Instrumental errors,

and b) Observational

errors.

a) Instrumentalerrors:

Instrumental errorsarecausedbyimperfectionsin instruments,wearand tear of

instrumentsduetocontinuoususeandtheir roughhandling. Instrumentsarethusrequiredtobe



testedforaccuracy, adjustedandcalibratedatfrequentintervals to ensurethat theresultsof

surveyingexercisesare wellwithin theprescribed limitsofaccuracyandtolerances.

b)Observationalerrors:

Observationalerrorsareintroducedbecauseofinvolvementofhuman factorinsurveying

process.Itshouldbeacceptedthatwheneverahumanelementisinvolved,theprocessresultwill

beinfluencedby theattitude,efficiency andperceptionofindividualhumanbeinginasubjective

manner. Thesecan beavoidedbypropertrainingofsurveyors,prescribingadequateandsuitable

precautions tobeundertakenineachobservationalandmeasurementprocess,andspecifying

properand detailed methodstatementsforperformingeachoperationoftheprocess.

Boththesetypesoferrors,i.e.instrumental and observational,canbefurtherclassifiedinto:

i. Grosserrors,

ii. Systematicerrors, and

iii. Accidentalorrandomerrors.

i) Grosserrors:

Grosserrorsormistakesareblundersthatoccurduetoinexperienceorcarelessnesson

thepart ofthesurveyor. In chain surveying,thesecould bedueto

�displacementorlossofpegsorarrows,providedtoidentifyandfixthelocationofvarious

typesofstationsandotherplacesofinterest.



�reading thechain or tapein awrong manner orusinganinstrumentinanincorrectway,and

�Wrongrecodingof measurementsintherecord book,e.g.field book.

Thereisno room for grosserrorsorblundersinthesurveyingprocesses.If grosserrorsare

detected,theentiresurveyingprocessandmeasurementsare requiredtoberepeatedafresh,

resultinginsubstantiallossoftimeandresources.Sucherrorscanbeavoidedbypropertraining

andtestingofsurveyors,adoptingstandard procedures,evento the

minutedetailsandcarryingout thesurveyworkwith utmostcare.

ii)Systematic errors:

Systematicerrorsfollow somespecificpatternaccordingtosome

mathematicalorphysical law.The errorcould be cumulative,i.e.occurringin the samedirection

and tends to accumulate affectingtheaccuracy ofmeasurementstoa greatextent.In

thecontextofchainsurveying, these could bedueto:

�Erroneouslengthof chain or tape (+ve or–ve),

�Erroneousranging,

�Links in chain notstraight (local bends) duetoroughhandlingortwistingof metallic tapes,

�Non-horizontallyofchain/tapeoverroughgroundterrain,

�Saginchain ortape, whenitisstretchedacrossa depressioninground,

�Variationin temperatureand/or dampness, and

�Variationin pull appliedduring measurement.

These errorscould be identified and adjusted and can be modeled.Suitable

corrections can beappliedto the measurements for obtaining greater accuracy. Following

aresome of the important correctionsapplied tomeasurementsusingchain or tape:

�CorrectionforErroneous Lengthof Chain/Tape:



Thechainsurveyingdependsonly onlinearmeasurementofdistances.Fortraversingonly

the errorsindistancemeasurementsareofimportanceandsignificance.Measuringdeviseeither

chainortapecaneitherbelongerorshorterthanthedesignatedlength.Themeasureddistance

willbesmallerthanthe actualifthelengthofchainislongerthan thedesignatedlength.Itwill be

largerthan the actual ifthe chain isshorter than the designated length. The actual measured

distance canbecorrected bythefollowingformula:

�L'�

TrueorCorrectDistance=� �X measured distance

�L�

where, L′=Actual incorrect lengthofchain,and

L= Designatedlengthofchain.

�CorrectionforTemperature:

Correctionfor temperatureisapplied if the temperature in thefield is more than

the temperatureatwhichthetape/chainwasstandardized.Thiscorrection(Ct)isgivenbythe

following

formula:

Ct��α (Tm��To)L

Where,α= Coefficient ofthermalexpansion,

Tm= Mean temperature inthefield duringmeasurement,

To= Standardtemperaturefor the tape,and

L=Measureddistance.



�CorrectionforPull:

�P��Po�L

CP=��

�AE �

Where,P=Pull appliedduring measurements(kg or

N), Po=Standardpull,

L=Measuredlength,

A=Cross-sectional areaof thetape(cm2ormm2),and

E=Young’smodulus ofelasticity(kg/cm2orN/mm2).

�CorrectionforSag:

Correctionforsagisappliedwhenthetapeisstretchedon supportsbetweentwopoints,it

takes the formofahorizontalcatenary. Thehorizontaldistancewillbelessthan the distancealong

thecurve.Thedifferencebetweenhorizontaldistanceandthemeasuredlengthalongcatenary is

calledsagcorrectionanditisalwaysnegative.

L�wL�2

CS=

24n2P2



Whenunit weightisgiven,

L�W�2

CS=

24n2P2

Where,L= thelengthof thetape(inm) suspendedbetween

thesupports, P=Pull appliedin kgor N, and

w=Weight ofthetapeinkg or N per m run.

W=Total weight oftapeinkg

n= Numberofspans

iii) RandomorAccidental Errors:

RandomorAccidentalerrorscan occurdue tolackofperfectionofhumaneyeandor

human behavior.Even the bestand efficientsurveyorcan have fatigue effectafterworking

forlong durationinstrenuousenvironmentcausingobservationalerrors.The

randomerrorscannotbe eliminated entirely,whateverprecautions areundertaken. These

may,however,occurin either direction and hence,tend to compensate and,

thus,arenotserious innature. These normallyfollow

thelawofchanceand,thus,canbeanalysedwiththehelpofprobability theory.Usingsuitable

probabilitydistribution functions,theseerrorscanthenbeadjusted,distributed amongvarious

measurementsandaccounted for.Each surveyingmethodorprocesscanbeassigneda reliability

factor (orriskfactor) foraccuracydependingontheanalysisofprobabilitybehavior.



3. AsurveylineABCcrossingariveranglescutsitsbanksatBandC.Todeterminethe width

BCoftheriver.Thefollowingoperationwascarriedout.A pointEwasestablishedonthe

perpendicularBE suchthat angle CEFis arightanglewhereFis apoint on thesurveyline.

If thechainageofFandBarerespectively1200mand1320mandthedistanceEBis90m.

Calculatethewidth of the riverandalsothechainageofC. (CO1-H1-

AUCApr/May2011)

BF=ChainageofB–Chainageof F

= 1320–1200

BF=120m

From ∆EBF,



tanBEF=

120

90

= 1.33

BEF=53O3’

�BEC��CEF��BEF

=90O- 53O3’

�BEC�36O57’

From∆BEC,

tan(36O57’)

=

CBCB

=

BE 90

CB=90X tan(36O57’)

CB= 67.69m

Thewidthoftheriver,CB = 67.69m

ChainageofC= chainageofB+ widthoftheriver



=1320+ 67.69

ChainageofC= 1387.69m



4. Explainthemethodsofchainingwhilethereare obstaclessuchasbuilding orriver.

(CO1-H1-AUC Nov/Dec2011) (CO1-H1-AUC May/June 2012)( CO1-H1-AUCApr/May2010)

Inthiscaseit is requiredtoprolong thechain linebeyond theobstacle andtofindthe

distance acrossit. Inthiscasethetypical obstacle is abuilding. Oneofthefollowingtwo

methods maybeadopted.

Firstmethod:

Onone sideofthechain lineAB, two pointsPandQareselected.Perpendicularsofequal

lengthPP’ and QQ’ areerected. ThelineP’Q’ isextended till thebuildingispassed. Onthe

extended line,two points R and Sareselected. The perpendicularat Rand

Saresoerectedsuch that RR’ =SS’= QQ’ = PP’.thenthepoints P’, Q’, R’and S’ will lie on

thesameline.ThenQ’R =

QR andthedistanceQ’R’ is measuredtoset QR, thenthelineisextended.

Second method:

Thismethodisalso equallyapplicable for thiscondition.Two pointsPandQonthechain

lineAB areselectedontheone sideofthechain line.A perpendicular QRiserectedat Q suchthat

QR = PR. PointsPandR arejointedand extendeduptoS. A perpendicularSV isset at S

suchthat PS =SV.OnthelineSVa point T ismarkedsuchthatST = SR.with

Vascentreandradius equal toQR cutanarcsuchthatPQ = QR=VT =UT. ThenU and

Vareonthechain lineAB. The distance RTismeasured. Thustheobstructedlength, QU= RT.



5. Describethe construction andworking ofanopticalsquarewith aneatsketch.

(CO1-H1-AUCApr/May2010)

It ismoreaccuratethanthecrossstaffanditcanbeusedfor locating objectssituatedat

largerdistances. It issmall and compacthandinstrument (Fig.8)andworksontheprinciple of

reflection. Generally itisa roundbrassboxabout5 cm in diameterand1.25 cm deep.There is

also a metal cover to protect it fromdust,moisture etc. Asshown infig. 8,it

consistsofhorizontal mirror (H)andindexmirror (1)placed atanangle of450 toeach other.

ThemirrorH ishalfsilveredand

theupperhalfisplain while themirror Iisfullysilvered.Therearethreeopeningsa,bandconthe

sides.LetAB isthechainlineand it isrequiredto locateanobjectOduring theprocessof

surveying. Theoptical squareisheldin suchamanner that arayoflightfromobject Opasses

throughslot c, strikesthemirror, getsreflectedand strikesthesilveredportionofthemirror

H.After being reflectedfromH, the raypassesthroughthe pin hole andbecomesvisible to

theeye. The



observerlooking throughthehole acandirectlysee theranging rodatBthroughtheun-silvered

portionof themirrorH and theimage of theranging rodplaced at O.Thus when both

theranging rodscoincide, thelineOD becomesperpendicular tothechainline.If

theydonotcoincide, the optical squarehastomove backandforthtoget thecorrect

positionofD.

Settingout PerpendicularLines:

A linehastobeset out perpendiculartothebaselinefrompeg(A).Peg (A)isnot onthe

base line.A long ropewith a loop at bothendsand ameasuring tapeareused. Theropeshould

be afewmetreslonger thanthedistancefrompeg(A)tothebaseline.



Step 1:

Oneloop oftherope is placedaroundpeg (A).Putapeg throughtheother loop oftherope

and makeacircle on thegroundwhile keeping the ropestraight.Thiscircle crossesthebase line

twice (seeFig.9). Pegs(B)and(C) areplaced wherethecircle crossesthebase line.

Step 2:

Peg (D) isplacedexactlyhalfwayin between pegs(B) and(C). Use ameasuring

tapeto determine thepositionofpeg (D). Pegs(D) and(A) form

thelineperpendiculartothebaselineand theangle between theline CD andthebase

lineisarightangle(seeFig.10).



6. A20msteel tapewasstandardized on flatground atatemperatureof20oCundera pull of

15kg.Thetapewasusedincatenaryatatemperatureof30oCunderapullof10kg.The

crosssectionalareaofthetapeis22mm2 anditstotalweightis400gm.Theyoung’s

modulusandcoefficientofthermalexpansionforsteelare21000kg/mm2 and11x10-6 /oC

respectively.Findthe correct distance.(AUCApr/May2010) Solution:

Given:

L= 20m;T0= 20oC;Tm= 30oC;Po=15kg; P=10kg; Area= 22 mm2;

W= 400gm = 0.4kg;α= 11x10-6;E= 21000kg /mm2

i) CorrectionforTemperature:

Ct=α (Tm-T0)L

=11x10-6(30–20)x20

Ct= 0.0022m

ii)CorrectionforPull:

�P��Po�L=�10�15 �

CP=��

�AE �

��X20

�22X21000�

CP= -0.000216

m iii) Sag Correction:

LW2



20X�0.4�2

Cs=

24n2P2

=

24X(1)2X(10)2

Cs= 0.00133m

Total correction=Ct+CP- Cs

= 0.0022+ (- 0.000216)–0.00133

Total correction=0.000654m

True length=Length+correction

=20+ 0.000654

Truelength= 20.000654m

7. Explainthemethodofranging byusing lineranger. (AUC Nov/Dec2011)



Itisasimpleinstrumentusedforfixingintermediatepointsonchainline.Inthisinstrument two

right-angledisoscelestriangularprisms areplaced one abovetheother.

Inordertoestablishapointinbetween theendstationsA andB thesurveyorholds the

instrumentattheleveloftheeyeandstandsapproximately inlinenearP.Raysoflight fromA

passesthroughtheupperprism getreflectedappearsto theeyeperpendiculartoAB.Similarly

anotherrayfromBreachestheeyeafterreflection.ThattheimagesofrangingrodsatstationA

andBappearinupperandlowerprismdirectly infrontofthesupervisor.Ifthealignmentiscorrect

boththeimagesappear oneabovetheotherina verticalline otherwise get separated.The



surveyorhastomoveperpendiculartochainlinetillhegetsthecorrectalignment.Thenthe

requiredpoint P isverticallybelowthecentreoftheinstrument.

The instrumentis very handy and simple to operate. It isquite useful to establish

intermediate pointsmorerapidlyand there isnonecessitytogototheendstations.

Adjustmentof lineranger:

Oneofthemirrorsorprismsiscommonlymadeadjustable.To testtheperpendicularity

between the reflecting surfaces, three poles are ranged very accurately with the help of a

theodolite. Thelinerangerisheldoverthemiddlepole.Theinstrumentwillbeinperfectadjustment

iftheimagesofthetwoendpolesappearinexactcoincidence.Ifnot,theyaremadetodoso turning

themovable prismbymeans of theadjustingscrew.

8. Determinethesagcorrectionfora30msteeltapeunderapullof80Nin3baysof10m

each.Theareaofthecrosssectionofthetapeis8mm2andtheunitweightofsteelmaybe

taken as77kN/m3. (AUC

Nov/Dec2011) Solution:

Given:

L= 30 m;n=3;P=80N; Area= 8mm2= 8 x 10-6m2;γ= 77kN/m3



Totalweightof tape = 77x103x8 x 10-6x10=6.16N

Cs=

LW2

24n2P

2

10X�6.16�2

=

24X�1�2X�80

�2

=0.00247 m

Cs=3x0.00247=0.00741m

True length= 30–0.00741

True length=29.993m

9. A andBaretwopoints ontheoppositesides ofapond.ThesurveyorestablishesalineAC

clearofthepondsuchthatB isvisible fromC.heestablishes anotherpointDonthe line CB

producedsothatthelineADisalsoclearofthepond.IfthedistancesAC,CB,BDandDA

are300m, 150 m,175mand250mrespectively.DeterminethedistanceAB.

(AUC Nov/Dec2011)



CD= CB + BD = 150+175= 325m

Applyingcosineformulae,�ACD



Cos ACD=

AC2 �CD2

�AD2

2ACXCD

3002 �3252

�2502

=

2X300X325

Cos ACD= 0.683

From�ACB,

Cos ACB=

Cos ACD=

AC2 �BC2

�AB2

2ACXBC

112500�AB2

90000

3002 �1502

�AB2

=

2X300X150

But�ACD

=�ACB



112500�AB2

0.683=

90000

AB2=51030

AB =225.89m

Thewidth of theriver,AB =225.89m

10.Explainthemeasurementoflengthwiththehelpofatape. (AUC Nov/Dec2010)

For accuratemeasurements thelengthsarenowmeasuredwith tapeand notwith

achain. Thefollowingprocedure isadopted.

�Letthelengthofa lineAB be measured, pointAbeing thestartingpoint.Placea ranging rod

behind thepointBsothatit isonthelinewith respect tothestartingpoint A.

�Thefollowerstands atthe pointA holdingone end ofthetape while theleadermoves ahead

holdingzeroendofthe tapeinonehandabundleofarrowsintheother.Whenhe reaches

approximatelyonetapelengthdistantfromA,the followerdirectshimforrangingintheline.

The tapeisthenpulledoutandwhippedgently tomakesure thatitsentirelengthliesalong

theline. Theleaderthenpushesthearrow intothe ground,oppositetozero. Thepinis

usuallyinclinedfromverticalabout20or30degrees,startingatrightanglestothelineso that

itsidesunder thetape,with its centre oppositethegraduationpointon thetape.

�Thefollowerthenreleaseshisendof thetape andthe twomoves forward alongtheline, the

leaderdraggingthetape.Whentheendofthetapereachesthearrowjustplaced,follower



callsout“tape”.Hethenpicksuptheendofthetapeandlinestheleaderinandthe

procedureisrepeatedasin step2.

�Whenthesecondarrowhasbeenestablishedby theleader,the followerpicksupthe first

arrow andboth thepersonsmoveaheadasdescribedinstep3. Theprocedureis repeated

untiltentapelengthshavebeenmeasured.thesurveyorrecordsthetransferofarrowsin

thefield book.

�Attheendoftheline,atB,thelastmeasurementwill generallybeapartialtapelength from

thelastarrow setto theendpointofthe line. The leaderholds theendofthetapeatBwhile

thefollowerpulls the tape back till itbecomestautandthenreadsagainstthearrow.

11.Explainthetraversingand plotting procedures of chainsurvey. (AUC May/June

2013) Traversing:

Traverseisamethodin thefield ofsurveying toestablish control networks. Traverse

networks involve placingsurveystations alongalineorpathoftravel,and then using the

previously surveyedpointsas abaseforobserving thenext point.

The methodin which thewhole workisdone with chain andtape iscalledchain

traversing. No anglemeasurement isused

andthedirectionsofthelinesarefixedentirelybylinear

measurementsAnglesfixedbylinearortiemeasurementsareknown aschain angles. The

method isunsuitableforaccurateworkand isgenerallyused ifananglemeasuring

instrumentsuchasa compass,sextantor theodolite is available.

Proceduresofchain survey:

Thechaintraversingis tofindouttheareaoftheoneblock bytraversingwith thechain. The

instrumentsused are Chain,Arrows, CrossStaff,Rangingrod, Pegsandhammer.

Thesteeltape istakenandtwo partiesaremade. Onepartystandsatthepointfromwhere



measurementisstartedand theotherpartygoestothepoint until which

measurementisrequired.

Chainingisdoneoffsetiscarriedoutatthecornerandatthesteps,usingacrossstuff.The

diagonalisalsomeasuredfor checkingpurposes.Theobservation ismadeandthedistance

observedis recorded, inthiswaywhole ofthebuildingismeasuredandeach length

isrecordedin thecopy.Then somescale is chosentorepresent thesemeasurementson

thefield bookand it is drawn on thefield booklikea plan.



Eachsideofthelengthcanbecalculatedand plinthareaof thebuildingiscalculatedby

using theabovefigure.

PlinthArea= ½(abxad) + ½ (bcxcd) + ½ (hgxhe) +½(texty)

Thebuildingcanbe divided into number of sections

andeachareaofthesectionis calculatedand added.

12.Explainthe fieldand officeworkin chain surveying? (AUC May/June 2013)

FieldandOfficework:

Thepracticeof surveyingactuallyboilsdown tofieldworkandoffice work. The

FIELDWORKconsistsoftaking measurements,collectingengineering data,andtesting

materials. TheOFFICEWORK includes taking careofthe computationanddrawing

thenecessary information forthepurposeofthesurvey.

FieldWork:

Field workisof primary importancein all typesofsurveys. Tobea skilledsurveyor,you

must spenda certainamountof timein thefield to acquire neededexperience. The

studyofthis trainingmanual will enable you to



understandtheunderlyingtheoryofsurveying,theinstruments and their uses,andthe

surveying methods.However,a high degreeofproficiency in actual surveying,as

inotherprofessions, depends largelyupon theduration,extent, and variationofyour actual

experience.

Youshould develop thehabitofSTUDYING theproblem

thoroughlybeforegoingintothe field, youshouldknowexactlywhatis tobedone;how youwill

doit;why youprefera certain approachoverotherpossible

solutions;andwhatinstrumentsandmaterialsyouwill need to accomplishtheproject.It

isessential thatyoudevelopSPEED and CONSISTENTACCURACY in all your fieldwork.

Thismeans thatyouwill needpracticein handling theinstruments, taking observations

andkeepingfield notes, and planning systematicmoves.

It isimportant thatyoualso develop thehabitofCORRECTNESS.Youshould

notaccept anymeasurement ascorrect withoutverification.Verification,

asmuchaspossible,should be different from theoriginal method usedinmeasurement.

Theprecisionof measurement must be consistent with

theacceptedstandardforaparticularpurposeof thesurvey.Fieldworkalso includes adjusting

theinstrumentsandcaringfor field equipment.Donot attempt toadjust any instrument unless

youunderstandtheworkingsorfunctionsofitsparts.Adjustmentofinstruments in

theearlystagesofyourcareer requiresclose supervision fromasenior EA.

OfficeWork:

Officeworkin surveyingconsistsof converting thefieldmeasurements intoa

usableformat. Theconversion ofcomputed, oftenmathematical,values

mayberequiredimmediatelyto continue



thework, or it maybedelayeduntil a series of field measurements

iscompleted.Althoughthese operationsare performed in thefield duringlapsesbetween

measurements, theycanalsobe consideredoffice work.Suchoperationsare normallydone to

savetime. Special equipment, such

as calculators, conversion tables, andsomedraftingequipmentisusedinmost office work.

Inoffice work, convertingfieldmeasurements(alsocalled reducing)involves

theprocessofcomputing, adjusting,andapplyingastandardrule to numerical values.

13.Explainhowyouwillconductchain surveyto measurealandparcelin agriculture field.

(CO1-H1-AUC May/June 2013)

Usingchainingandrangingthedistancebetweentwopointscanbemeasured.The

instrumentsrequired arechain, arrows,ranging rods,pegsandhammers.

Procedures:

Firstmarkastraightlineofastandardlengthonaflatfirmground.ThetwoendpointsAandBare

selectedonasurveylinewhichistobemeasured. A rangingrodiserectedatthepointB,while

thesurveyorstandswithanotherrodatpointA. A rodisestablishedatapointinlinewithABata

distancenotgreaterthanonechainlengthfromA. ThesurveyoratA thensignalstheassistantto

movetransversetothechainlinetillheislinewithAandB.Similarlyotherintermediatepointscan

beestablished.Thenbyusingchain,thedistanceismeasured.Tofindthepacinglength,we

shouldwalkalongthechainlineanditisfoundfrompacinglength.

Pacinglength=Distancebetweenthepoints/Noofsteps

Thedistancebetweentwo points= (Noofarrowx Nominal length+Fractional

length)m



Thedistancebetween two pointscanbecalculatedand alsosame procedure

isusedtofind theother sideof theline.Thefinally land parcel of agriculturalfield ismeasured.

Precautions:

�Surfaceshould besmooth and even.

�Surveyormust walkin straightline.

�Measuringtapemust bekeptstraightandhorizontal.

�Rangingshouldbeperformedformeasurementsgreaterthantapelength.

14.Explaintheconventionalsigns usedinchainsurveyingwithneatsketches.

(CO1-H1-AUC Nov/Dec2012)



15.Alinewasmeasured withasteeltape which wasexactly30mat25oCandatapullof15kg, the

temperature during the measurement was 35oC and the pull applied was 25 kg.

Assumingthetape tobesupportedatevery30m,calculatethe truelength,ifthecross

sectionalareaofthetape was0.020cm2,coefficientofthermalexpansionofthematerialper

oC=3 x10-6,modulesofelasticity(E)=2.1x 106kg/cm2andweight of tapematerial =0.8kg.

(CO1-H1-AUC Nov/Dec2012)



Solution:

Given:

L=30m;T0= 25oC;Tm= 35oC;Po=15kg;P=25kg;Area=0.020cm2;

W= 0.8kg;α= 3 x 10-6;E=2.1 x 106kg /cm2

i) CorrectionforTemperature:

Ct=α (Tm-T0)L

=3x10-6(35–25)x30

Ct= 0.0009m

iii)CorrectionforPull:

CP=

�P�Po�

L AE �25�15�X30

=

0.02X2.1X106

CP=0.00714m

iv)Sag Correction:

LW2

30X�0.8�2

Cs=

24n2P

2

=

24X�1�2X�25�

2

Cs= 0.00128m



Total correction=Ct+CP- Cs

= 0.0009+0.00714–0.00128

Total correction=0.00676

m

Truelength=Length+correction

= 20+ 0.00676

Truelength = 20.00676 m

16.Asurveyline EFGcrosses ariver,FandG being onthe nearanddistancebanks

respectively.StandingatS, a point60mmeasured perpendicularlyto EF fromF,the

bearings of G and Eare 325oand 230orespectively.EF being30m.Findthewidthofthe

river. (AUC

May/June 2012)



InΔ FSE, FE = 30mandFS=60m

30

tanESF=

60

�ESF=26O34’

�ESG

�FSG

=325O–230O= 95O

=95O–26O34’ =68O26’

NowfromΔ FSG,

FG = FS tan(68O26’)

= 60X tan(68O26’)

Widthoftheriver, FG=151.8m

17.Whatisawellconditionedtriangle?Whyit isnecessaryto make useofthem?

(AUC May/June 2012)



All well-conditioned triangle is onein which noincludedangle islessthan 30’ or

greater than 120’. Anequilateraltriangle isthebestconditioned triangleoranideal triangle.

Other examples ofwell-conditionedtrianglesareshown infigure.

Well-conditioned trianglesarerecommended because of their apexpointswhich

are verysharp and canbelocatedaccurately.Intheuseofwell-conditioned triangles, there is

no possibilityofrelative displacement oftheplottedpoint.Triangleswhich have

includedangles less than30’ andmorethan120’ arecalledasill-conditionedtriangles.



Thesetrianglesarenotpreferredin chain surveyingor triangulationsurveyas their apex

pointsarenot sharp andwell defined.Ifin certainfield conditionsiftheyare unavoidable

greatcare must betakenin chainingand plotting.

18.Explainthemethodsofdirect rangingindetail.(AUC Nov/Dec2009)

Whenintermediaterangingrodsare fixedonastraightlineby directobservation fromend

stations,theprocessisknownasdirectranging.Directrangingispossiblewhentheendstations

areintervisible.

AssumethatAandBtwoendstationsofchainline,wheretworangingrodsarealready

fixed.Supposeitis requiredto fixarangingrodattheintermediatepointPonthechainlineinsuch

awaythatthepointsA,P&Bareinsamestraightline. Thesurveyorstandsabout twometers

behindtherangingrod atAbylookingtowardslineAB.TheassistantholdsrangingrodatP

verticallyatarm’slengththerodshouldbeheldtightlybythethumbandforefinger.Nowthe

surveyordirecttheassistantto movetherangingrodtotheleftorrightuntil thethreerangingrods

comeexactly thesamestraightline.Therangingwillbeperfect,whenthethreerangingrods

coincideandappearasasinglerod. Whenthesurveyorissatisfiedthattherangingisprefect,he

signalstheassistanttofixtherangingrodontheground.Byfollowingthesameprocedure,the other

ranging rodsmaybefixedontheline.



19.Explainthemethodofreciprocal ranging in detail.(AUC Nov/Dec2010)(AUC Nov/Dec2009)

Indirectrangingisusedwhentheendstationsarenotintervisibleduetohighgroundora

hilloriftheendsaretoolong.Insuchcases,intermediatepointscanbe fixedonthesurveylineby a

processknown asreciprocal ranging.

Thevisionrangingandlinerangercan beadoptedonlywhentheendstationsareinter-

visible.However,inmany reallifesituations,thelineofsightbetweentwostationsisobstructedby

naturalor man-made objects (Figure),or theybeingtoo faraparttobe clearlyvisible.Undersuch

conditions,indirectorreciprocal rangingis resorted to.In this method,twointermediatepointsC1

andD1areselectedwhicharenotalongtheline ofsightAB(surveyline).StationsC1andD1are

approximately inlinesuchthatlineC1D1isapproximately paralleledtoAB.C1issosituatedthat

both D1andB are visiblefrom it, while from D1 bothA andC1canbesighted.



ThesurveyorsaresituatedatC1andD1originally.SurveyoratC1directssurveyoratD1

tomovesuchthatheisalignedindirectionC1Btooccupynew positionatD2.NextsurveyoratD2

directs thesurveyoratC1toalignalongline AD2tooccupy new positionC2.Thisprocessof

alignmentandrealignmentcontinuestillboththesurveyorsoccupypositionsCandDwhichare

situatedalong lineAB ensuring that surveylineisaligned alongACDB as shown inFigure.

20.Whatareoffsets?Howaretheytakenandrecorded?Plotthefollowingcrossstaffsurvey and

calculatethearea



Solution:

Skp Engineering College,Tiruvannamalai III SEM


Area1=

Area2=

x30x 36= 540m2

2

1 x30x30=450 m2

2

Area3=18x30=540m2

1

Area4= x18x15= 135m2

2

Area5=42x36 =1512m2

1

Area6=

Area7=

Area8=

x42x12= 252m2

2

1x24x48= 576m2

2

1x48x 45= 1080 m2

2

Total area=540+ 450+540+ 135+1512+ 252+576+ 1080

Total area= 5085m2



21.The followingcrossstaffsurveyand calculatethe area.

D

E 100

F120

370

270

240

125

100

125 C

90 B

A

Solution:



Area1=

Area2=

x125 x 120 = 7500m2

2

1 x100 x 90= 4500 m2

2

Area3= 140x90= 12600m2

1

Area4=

Area5=

x140 x 35=2450 m2

2

1x130 x 125 = 8125m2

2

Area6= 145x100 = 14500 m2

1

Area7=

Area8=

x145 x 20= 1450m2

2

1x100 x 100 = 5000 m2

2



Total

area=7500 +

4500+12600+

2450 +

8125+14500+

1450 + 5000

Totalar

ea=

56125

m2

Civil Engineering Department 52 Surveying I

UNIT 2

COMPASS AND PLANE TABLE SURVEYING

PART A

1. Define: Compass surveying. What are the objects of compass surveying?

(CO1-L1-AUC MAY/JUN 2013)

Compass surveying is the type of surveying in which the direction

of the survey lines are measured with a compass and the length of the

survey lines are measured with a tape or chain in the field.

2. Write the names of the instruments used in chain surveying.

(i). Instruments for the direct measurement of directions:

1. Surveyor’s compass.

2. Prismatic compass.

(ii).Instruments for the measurement of angles:

1. Sextant.

2. Theodolite.

3. Define: (a). True meridian

and bearing. True meridian:

(CO1-L1-AUC MAY/JUN 2013)



The line or plane passing through the geographical North Pole,

South Pole and any point on the surface of the earth, is known as true

meridian or geographical meridian. True meridian at a point is constant.

True bearing:

The angle between the true meridian and a survey line is known

as true bearing or Azimuth of the line.

(b). Magnetic meridian and

Bearing. Magnetic meridian :

Ma Magnetic Bearing:

The angle between the magnetic meridian and a survey line is

known as magnetic bearing or bearing .of the line. It changes with time.

gnetic meridian at a point is the direction indicated by freely suspended,

4. What do you understand by Whole circle bearing and quadrantal bearing of a

line? (CO1-L1-AUC MAY/JUN 2013)

Magnetic Bearings are designated by Whole circle bearing

system and quadrantal bearing system.

In Whole circle bearing system (WCB), the bearing of the line is measured with magnetic north in clockwise direction. It varies from 00 to 3600.



In quadrantal bearing system (Q.B or R.B) the bearing of the line is measured eastward or westward from north or south, whichever is nearer. The directions can be either clockwise or anticlockwise. It varies from 00 to 900.

5. Convert the whole circle bearing into reduced bearing: 500, 1760,

2100, 2320, 1500, 760,

Whole circle bearing

Reduced bearing

500 N 500 E.

1760

S (1800 – 1760)E = S 40 E

2100

S (2100 – 1800)W = S 300 W

2320

S (2320 – 1800)W = S 520 W

1500

S (1800 – 1500) E = S 300 E

760 N 760 E

3100

N (3600 – 3100) W = N 50 0 W

2420

S (2420 – 1800)W = S 620 W

6. Differentiate between Prismatic compass and

Surveyor’s compass with reference to reading and

tripod.

SI.No. Item Prismatic compass Surveyor’s compass



1. Reading (i). The reading is taken with a help of prism provided at the eye

slit.

(ii). Sighting and reading

taking can be done

(i). The reading is taken by directly seeing through the top of

the glass.

(ii). Sighting and reading

taking cannot be done 2. Tripod Tripod may or may not be

provided.

The instrument cannot be used

without a tripod.

7. The fore bearing of a line PQ is N 280 W. What is its back bearing? (CO1-L1-

AUC MAY/JUN 2013)

In quadrantal bearing (RB) system, the FB and BB are

numerically equal but the quadrants are just opposite.

The FB of a line PQ is N 280

W, Then its BB is S 280 E .

8. Define: Fore and Back bearing.

The bearing of a line is measured in the direction of the

progress of the survey is called the fore bearing of the (FB) line.

The bearing of a line is measured in the direction opposite to the survey is called the back bearing of the (BB) line.

BB = FB + 180 0 . (FB greater than 180 0, use - sign) (FB smaller than 180 0, use + sign)



9. The fore bearing of line AB is 155025’20”. Identify the back bearing

of the line AB in quadrantal system.

The fore bearing of line AB = 155025’20”.

The back bearing of line AB , BB = FB + 180 0

= 155025’20” + 180 0

= 335025’20” (WCB)

= N (3600 – 335025’20”) W

= N 24034’ 40’’ W

10. Define and distinguish between magnetic dip and

magnetic declination. Magnetic dip:

Due to the magnetic influence of the earth, the needle does not

remain in the balanced position. This inclination of the needle with the

horizontal is known as the dip of the magnetic needle. To balance the dip of

the needle, a rider (brass or silver coil) is provided along with it.

PART B

1.write a detail note about offset? (CO1-H1-AUC NOV/DEC 14)



These are the lateral measurements from the base line to fix the positions of the

different objects of the work with respect to base line. These are generally set at right

angle offsets. It can also be drawn with the help of a tape. There are two kinds of

offsets:

1) Perpendicular offsets,

and

2)Oblique offsets.

The measurements are taken at right angle to the survey line called perpendicular or right angled offsets.

The measurements which are not made at right angles to the survey line are called

oblique offsets or tie line offsets.

Procedure in chain survey:

The preliminary inspection of the area to be surveyed is called reconnaissance. The surveyor inspects the area to be surveyed, survey or prepares index sketch or key plan.

2.Marking Station:

Surveyor fixes up the required no stations at places from where maximum possible stations are possible.

3. Then he selects the way for passing the main line, which should be horizontal and

clean as possible and should pass approximately through the centre of work.

4. Then ranging roads are fixed on the

stations.

5. After fixing the stations, chaining could be

started.

6. Make ranging wherever

necessary.



7. Measure the change and

offset.

8. Enter in the field the book

2. write a Classification Of Surveying? (CO1-H1-AUC NOV/DEC 14)

Generally, surveying is divided into two major categories: plane and geodetic

surveying.

PLANE SURVEYING

PLANE SURVEYING is a process of surveying in which the portion of the

earth being surveyed is considered a plane. The term is used to designate survey

work in which the distances or areas involved are small enough that the curvature of

the earth can be disregarded without significant error. In general, the term of

limited extent. For small areas, precise results may be obtained with plane surveying

methods, but the accuracy and precision of such results will decrease as the area

surveyed increases in size. To make computations in plane surveying, you will use

formulas of plane trigonometry, algebra, and analytical geometry.

A great number of surveys are of the plane surveying type. Surveys for the

location and construction of highways and roads, canals, landing fields, and railroads

are classified under plane surveying. When it is realized that an arc of 10 mi is only

0.04 greater that its subtended chord; that a plane surface tangent to the spherical arc

has departed only about 8 in. at 1 mi from the point of tangency; and that the sum of

the angles of a spherical triangle is only 1 sec greater than the sum of the angles

of a plane triangle for a triangle having an area of approximately 75 sq mi on the

earth’s surface, it is just reasonable that the errors caused by the earth’s curvature be

considered only in precise surveys of large areas.

In this training manual, we will discuss primarily the methods used in plane

surveying rather than those used in geodetic surveying.

GEODETIC SURVEYING

GEODETIC SURVEYING is a process of surveying in which the shape and size of the

earth are considered. This type of survey is suited for large areas and long lines and



is used to find the precise location of basic points needed for establishing control

for other surveys. In geodetic surveys, the stations are normally long distances apart,

and more precise instruments and surveying methods are required for this type of

surveying than for plane surveying.

the surface of the earth are not along straight lines or planes, but on a curved surface.

Hence, in the computation of distances in geodetic surveys, allowances are made

for the earth’s minor and major diameters from which a spheroid of reference is

developed. The position of each geodetic station is related to this spheroid. The

positions are expressed as latitudes (angles north or south of the Equator) and

longitudes (angles east or west of a prime meridian) or as northings and castings on a

rectangular grid.

The methods used in geodetic surveying are beyond the scope of this training manual

TOPOGRAPHIC SURVEYS

The purpose of a TOPOGRAPHIC SURVEY is to gather survey data about the natural

and man-made features of the land, as well as its elevations. From this

information a three- dimensional map may be prepared. You may prepare the

topographic map in the office after collecting the field data or prepare it right away in

the field by plane table. The work usually consists of the following:

1. Establishing horizontal and vertical control that will serve as the framework of the

survey

2. Determining enough horizontal location and elevation (usually called side shots) of ground points to provide enough data for plotting when the map is prepared

3. Locating natural and man-made features that may be required by the purpose of

the survey

4. Computing distances, angles, and

elevations

5. Drawing the topographic map

Topographic surveys are commonly identified with horizontal and/or vertical control of

third- and lower-order accuracies.



ROUTE SURVEYS

The term route survey refers to surveys necessary for the location and construction of

lines of transportation or communication that continue across country for some

distance, such as highways, railroads, open-conduit systems, pipelines, and power

lines. Generally, the preliminary survey for this work takes the form of a topographic

survey. In the final stage, the work may consist of the following:

1. Locating the center line, usually marked by stakes at 100-ft intervals called

stations

2. Determining elevations along and across the center line for plotting profile and cross sections

3. Plotting the profile and cross sections and fixing the

grades

4. Computing the volumes of earthwork and preparing a mass

diagram

5. Staking out the extremities for cuts and

fills

6. Determining drainage areas to be used in the design of ditches and

culverts

7. Laying out structures, such as bridges and

culverts

8. Locating right-of-way boundaries, as well as staking out fence lines, if

necessary

SPECIAL SURVEYS

As mentioned earlier in this chapter, SPECIAL SURVEYS are conducted for a

specific purpose and with a special type of surveying equipment and methods. A brief

discussion of some of the special surveys familiar to you follows.



Land Surveys

LAND SURVEYS (sometimes called cadastral or property surveys) are

conducted to establish the exact location, boundaries, or subdivision of a tract of land

in any specified area. This type of survey requires professional registration in all

states. Presently, land surveys generally consist of the following chores:

1. Establishing markers or monuments to define and thereby preserve the boundaries of land belonging to a private concern, a corporation, or the government.

2. Relocating markers or monuments legally established by original surveys. This

requires examining previous survey records and retracing what was done. When

some markers or monuments are missing, they are reestablished following recognized

procedures, using whatever information is available.

3. Rerunning old land survey lines to determine their lengths and directions. As a result of the high cost of land, old lines are remeasured to get more precise measurements.

4. Subdividing landed estates into parcels of predetermined sizes and

shapes.

5. Calculating areas, distances, and directions and preparing the land map to

portray the survey data so that it can be used as a permanent record. 6. Writing a

technical description for deeds.

Control Surveys

CONTROL SURVEYS provide "basic control" or horizontal and vertical positions of

points to which supplementary surveys are adjusted. These types of surveys

(sometimes termed and traverse stations and the elevations of bench marks. These

control points are further used as References for hydrographic surveys of the coastal

waters; for topographic control; and for the control of many state, city, and private

surveys.

Horizontal and vertical controls generated by land (geodetic) surveys provide

coordinated position data for all surveyors. It is therefore necessary that these types of

surveys use first- order and second-order accuracies.



Hydrographic

Surveys

HYDROGRAPHIC SURVEYS are made to acquire data required to chart and/or map

shorelines and bottom depths of streams, rivers, lakes, reservoirs, and other larger

bodies of water. This type of survey is also of general importance to navigation and to

development of water resources for flood control, irrigation, electrical power, and water

supply.

As in other special surveys, several different types of electronic and radio-acoustical

instruments are used in hydrographic surveys. These special devices are commonly

used in determining water depths and location of objects on the bottom by a

method called taking SOUNDINGS. Soundings are taken by measuring the time

required for sound to travel downward and be reflected back to a receiver aboard a

vessel.

4.give the types of surveying? (CO1-H1-AUC NOV/DEC 14)

The practice of surveying actually boils down to fieldwork and office work. The

FIELDWORK consists of taking measurements, collecting engineering data, and

testing materials. The OFFICE WORK includes taking care of the computation and

drawing the necessary information for the purpose of the survey.

FIELDWORK

FIELDWORK is of primary importance in all types of surveys. To be a skilled surveyor,

you must spend a certain amount of time in the field to acquire needed experience.

The study of this training manual will enable you to understand the underlying theory

of surveying, the instruments and their uses, and the surveying methods. However, a

high degree of proficiency in actual surveying, as in other professions, depends largely

upon the duration, extent, and variation of your actual experience.

You should develop the habit of STUDYING the problem thoroughly before going into

the field, You should know exactly what is to be done; how you will do it; why you



prefer a certain approach over other possible solutions; and what instruments and

materials you will need to accomplish the project.

It is essential that you develop SPEED and CONSISTENT ACCURACY in all

your fieldwork. This means that you will need practice in handling the instruments,

taking observations and keeping field notes, and planning systematic moves.

It is important that you also develop the habit of CORRECTNESS. You should not

accept any measurement as correct without verification. Verification, as much as

possible, should be different from the original method used in measurement. The

precision of measurement must be consistent with the accepted standard for a

particular purpose of the survey.

Fieldwork also includes adjusting the instruments and caring for field equipment. Do

not attempt to adjust any instrument unless you understand the workings or functions

of its parts. Adjustment of instruments in the early stages of your career requires close

supervision from a senior EA.

Factors Affecting

Fieldwork

The surveyor must constantly be alert to the different conditions encountered in the

field. Physical factors, such as TERRAIN AND WEATHER CONDITIONS, affect

each field survey in varying degrees. Measurements using telescopes can be

stopped by fog or mist. Swamps and flood plains under high water can impede taping

surveys. Sights over open water or fields of flat, unbroken terrain create ambiguities in

measurements using microwave equipment. The lengths of light-wave distance in

measurements are reduced in bright

sunlight. Generally, reconnaissance will predetermine the conditions and alert the survey party to the best method to use and the rate of progress to expect.

The STATE OF PERSONNEL TECHNICAL READINESS is another factor affecting

fieldwork. As you gain experience in handling various surveying instruments, you

can shorten survey time and avoid errors that would require resurvey.



The PURPOSE AND TYPE OF SURVEY are primary factors in determining the

accuracy requirements. First-order triangulation, which becomes the basis or

"control" of future surveys, is made to high-accuracy standards. At the other

extreme, cuts and fills for a highway survey carry accuracy standards of a much

lower degree. In some construction surveys, normally inaccessible distances must

be computed. The distance is computed by means of trigonometry, using the

angles and the one distance that can be measured. The measurements must be

made to a high degree of precision to maintain accuracy in the computed

distance.

So, then, the purpose of the survey determines the accuracy requirements. The

required accuracy, in turn, influences the selection of instruments and procedures. For

instance, comparatively rough procedures can be used in measuring for earthmoving,

but grade and alignment of a highway have to be much more precise, and they,

therefore, require more accurate measurements. Each increase in precision also

increases the time required to make the measurement, since greater care and more

observations will be taken. Each survey measurement will be in error to the extent that

no measurement is ever exact. The errors are classified as systematic and accidental

and are explained in the latter part of this text. Besides errors, survey measurements

are subject to mistakes or blunders. These arise from misunderstanding of the

problem, poor judgment, confusion on the part of the surveyor, or simply from an

oversight. By working out a systematic procedure, the surveyor will often detect a

mistake when some operation seems out of place. The procedure will be an

advantage in setting up the equipment, in making observations, in recording field

notes, and in making computations.

Survey speed is not the result of hurrying; it is the result of saving time through the

following factors:

1. The skill of the surveyor in handling the

instruments



sunlight. Generally, reconnaissance will predetermine the conditions and alert the survey party to the best method to use and the rate of progress to expect.

The STATE OF PERSONNEL TECHNICAL READINESS is another factor affecting

fieldwork. As you gain experience in handling various surveying instruments, you

can shorten survey time and avoid errors that would require resurvey.

The PURPOSE AND TYPE OF SURVEY are primary factors in determining the

accuracy requirements. First-order triangulation, which becomes the basis or

"control" of future surveys, is made to high-accuracy standards. At the other

extreme, cuts and fills for a highway survey carry accuracy standards of a much

lower degree. In some construction surveys, normally inaccessible distances must

be computed. The distance is computed by means of trigonometry, using the

angles and the one distance that can be measured. The measurements must be

made to a high degree of precision to maintain accuracy in the computed

distance.

So, then, the purpose of the survey determines the accuracy requirements. The

required accuracy, in turn, influences the selection of instruments and procedures. For

instance, comparatively rough procedures can be used in measuring for earthmoving,

but grade and alignment of a highway have to be much more precise, and they,

therefore, require more accurate measurements. Each increase in precision also

increases the time required to make the measurement, since greater care and more

observations will be taken. Each survey measurement will be in error to the extent that

no measurement is ever exact. The errors are classified as systematic and accidental

and are explained in the latter part of this text. Besides errors, survey measurements

are subject to mistakes or blunders. These arise from misunderstanding of the

problem, poor judgment, confusion on the part of the surveyor, or simply from an

oversight. By working out a systematic procedure, the surveyor will often detect a

mistake when some operation seems out of place. The procedure will be an

advantage in setting up the equipment, in making observations, in recording field

notes, and in making computations.



Survey speed is not the result of hurrying; it is the result of saving time through the

following factors:

1. The skill of the surveyor in handling the

instruments

2. The intelligent planning and preparation of the

work

3. The process of making only those measurements that are consistent with the accuracy requirements

Experience is of great value, but in the final analysis, it is the exercise of a good,

mature, and competent degree of common sense that makes the difference between

a good surveyor and an exceptional surveyor.

Field Survey

Parties

The size of a field survey party depends upon the survey requirements, the equipment available, the method of survey, and the number of personnel needed forperformingthe

different functions. Four typical field survey parties commonly used in the SEABEEs

are briefly described in this section: a level party, a transit party, a stadia party, and a

plane table party.

LEVEL PARTY.— The smallest leveling party consists of two persons: an

instrumentman and a rodman. This type of organization requires the instrumentman to

act as note keeper. The party may need another recorder and one or more extra

rodmen to improve the efficiency of the different leveling operations. The addition of

the rodmen eliminates the waiting periods while one person moves from point to

point, and the addition of a recorder allows the instrumentman to take readings

as soon as the rodmen are in position. When leveling operations are run along

with other control surveys, the leveling party may be organized as part of a

combined party with personnel assuming dual duties, as required by the work load

and as designated by the party chief.



UNIT-3

LEVELLING AND APPLICATIONS

PART–A

1. What do you mean bycontourinterval? (CO1-L1-

AUCApr/May2011)

TheverticaldistancebetweenanytwoconsecutivecontoursiscalledContourinterval.The

contour interval iskeptconstantfor acontour plan.

2. Define bench mark. (CO1-L1-AUCApr/May2011)

Benchmarkisarelativelypermanent pointofreferencewhoseelevationwithrespecttosome

assumeddatum isknown.

3. What isprofilelevelling? Stateitsapplication. (CO1-L1-

AUCNov/Dec2011)

Whenlevellingexerciseisundertakenalongasurveyline,itistermedasprofilelevelling.

E.g.Decidingtherouteofaroador railwayline,centrelineofapipe/gasline,power/telephonelines

etc.,

4. Statethenecessityofmaking,balancing ofbacksightand foresight. (CO1-L1-AUCNov/Dec2011)



Aturningpointor

changepointdenotesthepositionatwhichbothforesightandbacksightreadingsaretakenbefo

reshiftingoflevel instrument.Anywell definedandstablepointcanbe

selectedaschangepoint,e.g.boundarystone,benchmark.

5. Statethelimitation oftheprismoidal formula. (CO1-L1-AUCApr/May2010)

Volume =(d/3) x[(A1+An)+4(A2+ A4+ A6+……+An-1)+2(A3+A5+…..+An-2)]

6. What ischecklevelling? (CO1-L1-

AUCApr/May2010)

Itis normal torunalineoflevelstoreturntostartstationafter theendofeachdaysworkfor the

purposeofcheckingthe accuracyandreliabilityofthemeasurementsandrecordingcarriedout

onthatparticular day.Thisistermedchecklevelling.

7. Definecontour. (CO1-L1-AUCNov/Dec2010)

Acontour isanimaginarylineonthegroundjoiningthepoints of equalelevation.

(Or)

Acontour isalineinwhichthesurfaceof groundisintersectedbyalevel surface.

Skp Engineering College,Tiruvannamalai


8. Writethetypesofbench mark.

AUCNov/Dec2010)

GTSbenchmarks

Permanentbench marks

Temporary benchmarks

Arbitrarybench marks

9. What do you mean by flyand

AUCMay/June2013) Flylevel

Whenthereareobstruction

thepurposeistoestablishbench

Checklevelling:

Itis normal torunalineof

purposeofcheckingthe acc

onthatparticular day.Thisisterm

10.Explain theuseof DumpyandMay/June2013)

DumpyLevel:

Itismostcommonlyusedin

Simpler constructionwith

Fewer adjustmentstobem

Longer lifeoftheadjustme

Tiltinglevel:


71

.

ks

ks

nd checklevelling?

lling:

onsinthelineofsight,thedistancebetweenstatio

hmarks,thisprocessisadopted.Thisistermedas

flevelstoreturntostartstationafter theendofea

ccuracyandreliabilityofthemeasurementsand

rmedchecklevelling.

ndTilting levels.

nengineeringsurveys.

hfewer movableparts.

made.

ents.

III SEM

surveying I

. (CO1-L1-

? (CO1-L1-

onsistoolargeor

s“flylevelling”.

achdaysworkfor the

recordingcarriedout

(CO1-L1-AUC



Itisusedfor precisionleve

Levellingcanbedonemuch

Don’ttakesomanyreading

11.Stateany fourtypesoflevelling

AUCNov/Dec2012)

Atelescopetoprovidelineo

Alevel tubetomaketheline

Alevellingheadtobringthe

Atripodtosupporttheinstrum

12.What ismeantbychangepoint

AUCNov/Dec2012)

Achangepointdenotesthepo

beforeshiftingoflevel instrumen


72

elling.

chquicker.

ngsfromoneinstrumentsetting.

nginstrument.

ofsight.

eofsighthorizontal.

ebubbleinitscentreofrun.

ment.

ntin levelling?

positionatwhichbothforesightandbacksightrea

nt.

III SEM

surveying I

. (CO1-L1-

? (CO1-L1-

adingsaretaken



13.What is foresight? (CO1-L1-

AUCNov/Dec2009)

Theforesightisthestaffreadingofthepointwhoseelevationisrequiredtobeobtained,

particularlyatachangepoint.Itisthelaststaffreadingatthestationbeforetheinstrumentisshifted

toanew station.

14.What isbacksight? (CO1-L1-

AUCNov/Dec2009)

Thestaffreadingtakenatapointofknownor predeterminedelevation.Thebacksightis thefirst

staffreadingtakenafter settingtheinstrumentatspecifiedsurveystation.

15.What ismeantbylongitudinalsectioning? (CO1-L1-AUC May/June2012)

Theprocessofdeterminingtheelevationofpointsatshortmeasuredintervalsalongafixed

line.Thefixedlinemaybestraightlineorseriesofstraightlinesconnectedbycurves.Itistermed

asLongitudinalsectioning.



PART–B

1. Theoffsetstakenat5mintervalsfromachainlinetoacurvedboundaryare:0,4.6,6.5,6.8,

5.2,3.5,2.2m.calculatetheareabetweenthechainline,thecurvedboundarylineandthe end

offsetsusing Simpsonsrule.

(VAUCApr/May2011) Solution:

UsingSimpsonsrule,

Area= (d/3)x[(Oo+ O6)+4(O1+ O3+O5)+2 (O2+O4)]

=(5/3) x[(O+2.2) +4(4.6+6.8+3.5) +2(6.5+5.2)]

= 1.67[2.2+4(14.9) +2(11.7)]



Area=142.28m2

2. Definecontoursand givecharacteristicsofcontours.

(AUCApr/May2011) Contours:

Acontour isanimaginarylineonthegroundpassingthroughpoints ofequal elevation.

CharacteristicsofContourLines

Characteristics ofcontour

linesarehelpfulinplottingandinterpretationofvariousfeaturesin the

map.Thesecharacteristicsareasfollows:



(a) Contour lineisalinejoiningpoints ofsameelevation;henceallpoints ofcontour lineshave

sameelevation.Theelevationofacontour iswrittenclosetothecontour.

(b) Twocontour lines of

differentelevationscannotintersecteachotherexceptincaseofan overhangingcliff or

acave(Figure1).

(c) Incaseofavertical cliffcontour lines of differentelevationscanjointoform onesingleline.

(d) Horizontalequivalentofcontoursindicatesthetopographyofthearea.Theuniformlyspaced

contourlinesindicateauniform slope,whilestraightandequallyspacedcontour linesindicatea

planesurface.Contour linesclosedtogether indicatesteepslope,whileagentleslopeis

indicatedwhencontour linesarefarapart.



(e) Acontour linecannotendanywhereandmustcloseuponitself,thoughnotnecessarilywithin

thelimitsofthemap.

(f) Asetofclosecontourswithhigherfiguresoutsideandlowerfiguresinsideindicateadepression

or lake,whereasasetofclosecontourswithhigherfiguresinsideandlowerfiguresoutside

indicateahillock.



(g) Contour linescrossawater shed(or ridgeline)andavalleylineatrightangles.Incaseofridge

line,theyform curves ofU-shapeacrossitwithconcavesideofthecurvetowardshigher

ground,whereasincaseofvalleyline,theyform sharpcurves ofV-shapeacrossitwithconvex

sideofcurvetowardshigher ground.

3. Explain

i. Reciprocallevelling

ii. Flylevelling

iii. Differentiallevelling

iv. Simplelevellingand statewhereeach isused. (CO1-H1-

AUCApr/May2011)

i) Reciprocallevelling:

Itisthe methodoflevellinginwhich thedifferenceinelevation between two pointsis

accuratelydeterminedbytwosetsofreciprocal observationswhenitisnot possibletoset upthe

levelbetweenthetwopoints.

Whenitis necessarytocarrylevellingacrossariver or any obstaclerequiringalongsight

betweentwopointssosituatedthatnoplacefor thelevelcanbefoundfromwhichthelengthsof

foresightandbacksightwill beevenapproximatelyequal.

Itmustbeusedtoobtainaccuracyandtoeliminate



Error ininstrumentadjustment.

Combinedeffectofearth’scurvatureandrefractionoftheatmosphere.

Variationsintheaveragerefraction.

ii) Differentiallevelling(Flylevelling):

Theoperationoflevellingtodeterminetheelevationofpointsatsomedistanceapartis

calledDifferentiallevelling.

Itisusuallyaccomplishedbydirectlevelling. Whentwopointsareatsuchadistancefrom

eachotherthattheycannotbewithinrangeofthelevelat thesametime.Thedifferencein

elevationisnotfoundbysinglesettingbutthedistancebetweenthepointsisdividedintwostages by

turningpointsonwhichthestaffisheld.Thedifferenceof elevationof eachofsucceedingpair of

suchturningpointsisfoundbyseparatesettingupofthelevel.

The image part with

relationship ID rId50 was not found i…

The image part with relationship ID rId51 was not found i…




Thisisalsotermedas“flylevelling”.

iv) Simplelevelling:

Whenthedifferenceinelevationbetweenanytwopointsisdeterminedfrom asinglesetup

bybacksightingononepointandforesightingontheother.Theerrorduetononparallelismofline

ofcollimationand axisofthebubbletube.Alsotheerrorduetocurvatureandrefractionmaybe

eliminatedifthelengthsoftwosightscanbemadeequal.

Ifthebacksightandforesightdistancesarebalancedthedifferenceinelevationbetween

two pointscan be directly calculated bytaking differenceofthetworeadings.Thereis

nocorrection fortheinclinationof thelineof sight,correction forcurvature and correction

forrefraction is necessary.



4. Followingreadingswereobservedsuccessivelywithalevellinginstrument.Theinstrument

wasshiftedafterfifthandeleventhreadings0.585,1.010,1.735,3.295,3.775,0.350,1.300,

1.795, 2.575,3.375, 3.895,1.735,0.635and 1.605.Drawup apageoflevelbookand

determine theR.L of variouspointsif theRL of thepointon which thefirst reading was

taken is

135.00m.

(AUCNov/Dec2011) Solution:

Station B.S I.S F.S Rise Fall R.L

A 0.585 135.000

1.010 0.425 134.575

1.735 0.725 133.850

3.295 1.560 132.290

B 0.350 3.775 0.480 131.810

1.300 0.950 130.860

1.795 0.495 130.365

2.575 0.780 129.585



3.375 0.800 128.785

C 1.735 3.895 0.520 128.265

0.635 1.1 129.365

1.605 0.970 128.395

∑B.S=2.670 ∑F.S=9.275 ∑Rise= 1.1 ∑Fall= 7.705

Check:

∑B.S–∑F.S=2.670-9.275=- 6.605

∑Rise–∑Fall=1.1-7.705=-6.605

LastR.L –FirstR.L= 128.395-135.000=- 6.605

Fall= 6.605

5. Explain thedirect methodsofcontouring

DirectMethod:

Inthismethod,thecontour tobeplottedisactuallylocatedonthegroundwiththehelpofa

level or handlevel bymarkingvariouspointsonthecontour.Thesepointsaresurveyedandplotted

todrawthecontoursthroughthemontheplan.Thoughthemethodisslowandtediousbutitis

mostaccurateandisusedfor contouringsmall areaswithgreataccuracy.

Incontouring,fieldworkconsistsofhorizontal andvertical control.Forasmall area,horizontal

control canbeperformedbyachainor tape,whileforalargeareacompass,theodoliteor aplanetable

canbeemployed.For vertical contour,alevel andstaff orahandlevelmaybeused.



i) VerticalControlbyLeveland Staff:

Aseries ofpointshavingsameelevationarelocatedonthegroundinthismethod.An

instrumentstationonthegroundisselectedsothatitcommandsaview ofmostoftheareastobe

surveyed.Heightoftheinstrumentcanbefixedsightinganearestbenchmark.Staffreadingis

calculatedfor aparticular contourelevation.Thestaffmanisdirectedtomoveleftor rightalongthe

expectedcontour until therequired readingisobserved.Aseriesofpointshavingsameelevation

asshownbythesamestaffreadingareplottedandjoinedtogetasmoothcurve.

ii) VerticalControlbyHand Level:

Thesameprincipleasusedinlevelandstaffmethodisemployedinthismethodalso.This

methodisveryrapidincomparisontotheformermethod.Ahandlevel maybeusedtogetan

indicationofthehorizontal linefromtheeyeoftheobserver.Alevel staff orapolehavingzeromark

attheheightoftheobserver’seyewhichisgraduatedupanddownfrom thispointisusedinthis

method.Themanwiththeinstrumentstandsoverthebenchmarkandthestaffmanismovedtoa

pointonthecontour tobeplotted.Assoonasthemanwithinstrumentobservestherequiredstaff

readingforaparticular contourheinstructsthestaffmantostopandlocatesthepositionofthe point.



6. Aseriesofoffsetsweretakenfromachain lineto acurved boundarylineat intervalsof15m

inthefollowingorder0,2.65,3.80,3.70,4.65,3.60,4.95and5.85m.computethearea

betweenthechainline,curvedboundaryandendoffsetsbytrapezoidal ruleandSimpsons)

Solution:

Using trapezoidalrule:

Area=[{(Oo+O7)/2} +O1+O2+O3+O4+O5+O6]xd

=[{(0+5.85)/2}+2.65+3.80+3.70+4.65+3.60+4.95]x15

Area=394.13m2

Using Simpsonsrule:

Hereniseven,

UptoseventhordinatesolvebyusingSimpsonsruleand

Lasttwoordinatessolvebyusingtrapezoidal rule

Area1=(d/3) x[(Oo+O6)+4 (O1+O3+O5)+2(O2+O4)]

=(15/3) x[(O+4.95) +4(2.65+3.70+3.60) +2(3.80+4.65)]



Area1= 308.25m2

Area2={(O6+O7)/2}xd

={(4.95+5.85)/ 2}x15

= 81m2

Area=Area 1+Area 2=308.25+ 81

Area=389.25m2

7. Thefollowingconsecutivereadingsweretakenwithadumpylevel and4mlevellingstaffon

acontinuouslyslopinggroundat30mintervals.0.680,1.455,1.855,2.330,2.885,3.380,

1.055,1.860,2.265,3.540,0.835,0.945,1.530and 2.250.RL of thestarting pointwas

80.750m.

I. Ruleout apageofalevelbookand entertheabovereadings.

II. DeterminetheRL of variousstaff stations.

III. Estimateaveragegradientofground measured.



Solution:


A 0.680 80.750

1.455 0.775 79.975

1.855 0.400 79.575

2.330 0.475 79.100

2.885 0.555 78.545

B 1.055 3.380 0.495 78.050

1.860 0.805 77.245

2.265 0.405 76.840

C 0.835 3.540 1.275 75.565

0.945 0.110 75.455

1.530 0.585 74.870

2.250 0.720 74.150

∑B.S=2.570 ∑F.S=9.170 ∑Rise=0 ∑Fall= 6.600

Check

:

∑B.S–∑F.S=2.570-9.170=- 6.600

∑Rise–∑Fall =0 –6.600=-6.600

LastR.L –FirstR.L= 74.150–80.750=-6.600

Fall= 6.600

Gradient

=

6.6

30X12



Gradient

=0.0183

Slope=1in 55

8. Discusstheeffectsofcurvatureandrefractioninlevellingandderivetheexpressionfor

thesecorrections. (CO1-H1-

AUCApr/May2010) Effects of Curvature:

BCisthedeparturefromthelevelline.Actuallythestaffreadingshouldhavebeentaken

atBwherethelevellinecutsthestaff,butsincethelevelprovides onlythe horizontallineofsight,

thestaffreadingis takenatthepointC.thus theapparentstaffreadingismoreandthereforethe

objectappearstobelowerthanreally.Thecorrectionforcurvatureisnegativeasappliedtothe

staffreadingitsnumerical valuebeingequal totheamountBC.TofindthevalueBCwehave

OC2=OA2+AC2,AngleCAObeing90o

LetBC =CC=correctionfor curvature

AB=d= horizontaldistancebetweenAandB



AO=R =radiusofearthinthesameunitasthatofd

(R +Cc)2=R2+ d2 (or)

R2+2RCc+Cc2=R2+ d2

Cc(2R+Cc)= d2 (or)

Cc=

d2

d2

=

2R CC2R

(NeglectingCcincomparisonto2R)

Tofindthecurvaturecorrection,dividethesquareofthelengthofsightby earth’sdiameter.

BothdandRmaybetakeninthesameunits,whentheanswerswillalsobeintermsofthatunit.

Theradiusoftheearthcanbetakenequalto6370km.ifdistobeinkmandR=6370km,Ccwill

beinmetres.

Effectsof Refraction:

Figure:Curvatureand Refraction

Theeffectofrefractionisthesameasiftheline ofsightwascurveddownwardorconcavetowards the

earth’ssurface andhencetherodreadingisdecreased.Therefore,theeffectofrefractionisto



2

maketheobjectsappearhigherthantheyreally arc.Thecorrectionasappliedtostaffreadingsis

positive. The refraction curve is irregular because of varying atmospheric conditions, but

for averageconditionsitisassumedtohaveadiameter aboutseventimesthatoftheearth.

d2

Thecorrectionofrefraction,Cr=

14R

(positive)

=0.01121d2meters,whendisinkm.

Thecorrectionduetocurvatureandrefractionwill begivenby

C= d

-

2R

d2

14R

3d2

=

7R

(negative)

=0.06728d2meters,dbeinginkm.

ThecorrespondingvaluesofthecorrectionsinEnglishunitsare:

2d2

CC= = 0.667d2feet

3



Cr=

C =

2d2

21

4d2

7

= 0.095d2feet

= 0.572d2feet

Wheredisinmilesandradiusofearth=3958 miles.

9. Thefollowingstaffreadingwereobservedsuccessivelywithaleveltheinstrumenthaving

beenmovedafterthird,sixthandeightreading2.228,1.606, 0.988,2.090,2.864,1.262, 0.602,

1.982,1.044,2.684m entertheabovereadinginapageoflevelbookandcalculateRLofthe

first reading was taken with astaff held on bench markof432.384m.

(CO1-H1-AUC Nov/Dec2010) (CO1-H1-AUCMay/June2013)

Solution:


A 2.228 432.384

1.606 0.622 433.006

B 2.090 0.988 0.618 433.624

2.864 0.774 432.850

C 0.602 1.262 1.602 434.452

D 1.044 1.982 1.380 433.072

2.684 1.640 431.432



∑B.S=5.964 ∑F.S=6.916 ∑Rise=2.842 ∑Fall= 3.794

Check

:

∑B.S–∑F.S=5.964–6.916=-0.952

∑Rise–∑Fall=2.842–3.794=- 0.952

LastR.L –FirstR.L=431.432 –432.384=- 0.952

Fall= 0.952

10.Explain theindirectmethodsoflocating contours.

(CO1-H1-AUCApr/May2010

Indirect Methods:

Indirectmethodsarequicker,cheaperandlesslaboriousthandirectmethod.Inthis

method,aseries ofguidepointsareselectedalongasystem ofstraightlinesandtheir elevations

aredetermined.Thesepointsarethenplottedandcontoursaredrawnbyinterpolation.Theguide

pointsgenerallyarenotthepointsonthecontourstobelocatedexceptincaseofacoincidence. For

plottingofcontours,theinterpolationisdonewiththeassumptionthattheslopebetweenany



twoadjacentguidepointsisuniform.Someoftheindirect methods oflocatinggroundpointsare

givenbelow.

i)MethodsofSquares:

Thismethodisverysuitablewhentheareatobesurveyedissmall.Thismethodisalso

calledcoordinatemethodoflocatingcontours.Theareatobesurveyedisdividedintoanumberof

squaresformingagrid.Thesideofasquaremayvaryfrom5to20mdependinguponthenatureof

thecontour andcontour interval.Theelevations ofthecornerofsquaresarethendeterminedby

usingalevelandastaff.Thelevelsaretheninterpolatedandcontour linesaredrawn.Sometimes

rectanglesmayalsobeusedinplaceofsquares.

ii)Methodsof Cross-sections:

Thismethodisgenerallyusedin rootsurveys.Cross-sectionsareruntransversetothe

centrelineofacanal, roadandrailwayetc.Thespacingofcross-sectionsbasicallydependonthe

nature ofterrainandthecontour interval.The reducedlevel ofvariouspointsalongthesectionline

areplottedontheplanandthecontoursarethendrawnbyinterpolation.



iii) TacheometricMethod:

Thismethodissuitableforhillyareas.Inthismethod,anumber oflinesaresetout radiating

atagivenangular intervalfromdifferenttraversestations.Therepresentativepointsontheselines

arelocatedinthefieldbyobservingverticalanglesandthestaffreadingofthestadiawiresofa

tacheometer.Theelevationsandthedistances ofthesepointsarecalculatedandplottedandthen

contour linesaredrawnbyinterpolation.



11.Explain themethod of profilelevelling. (CO1-H1-AUCMay/June2013)

(AUCNov/Dec2009)

i)Longitudinal

ProfileLevellingii)

CrossSectionalProfiling

i) LongitudinalProfileLevelling:

Letthecentral lineofrequiredroutebeABCDasshowninFigure9.Notethatthechange

pointsA,B,C,Detcareabout30m to70mapart,notmorethan100m innormal conditions.Staff

intermediatestations,e.g.1,2...11etc.areusually5to20mdistant.Theinstrumentissetupata

suitablefirmground(sayO),properlylevelledandadjusted,from whichlargenumber ofstaff

stationscanbecommanded.Backsightisthentakenonthebench marktodetermineHI,the

reducedlevel oflineofcollimationatinstrumentstationO.

Staffreadingsarethentakenstarting fromstationA followedbyreadingsatpredetermined

intervals of5m or 10m,measuringthedistanceA-1,1-2etc.bystretchingthechainonalignedline



AB.Inadditiontointermediatestations1,2, 3etc.,readingsarealsotakenatcriticalorimportant

pointsontheground,i.e. pointsindicatingchangeofslopeor other importantfeatures(e.g.sp1,sp

2etc.).

Whenthelengthoflineofsightexceedsvisibilitylimit,e.g. about 100m orso, orifthereis

someobstructioninthelineofsight,theinstrumentisrequiredtobeshiftedtonewposition(sayO).

ForesightonstaffstationBistakenfrominstrumentstationO1 beforeshiftingtheinstrumentfrom

positionO1toO2.Whentheinstrumentisset,levelledandadjustedatO2,thefirstreadingrecorded

fromO2 willbethebacksightatB.ThiswilldecidetheRLofnewlyestablishedcollimationplane.

Thedistanceofintermediateandspecial points arecontinuedtobemeasuredalonglineBCand

levelsreadateachofthesestations.Previously establishedbenchmarksareimportant points on

whichstaffreadingsarenecessarilytakenasacheckonlevelmeasuringprocess.Benchmarks

canalsobeusedaschangepoints.



Toplotthelongitudinalprofileofthegroundalongthesurveyline, firststepwouldbetofixa

datumlineandmarkingthechainagesoftheintermediate,special andchangepointsonitata

suitablescale.Verticallinesarethendrawnonthischainagelineat eachintermediate,special and

changepoints.Therespectivelevels arethenmarkedontheselines.Thelinejoiningtheseplotted

pointsrepresents thelongitudinal groundprofile.

ii) CrossSectionalProfiling:

Theprojectfacilitywhetheritishighway,railway,pipeline,ortransmissionline,willhave

certainwidth.Hence,inadditiontoobtaininginformationalongthelongitudinal section,itisalso

necessary togather useful informationuptodesiredtransversedistanceonbothsideoftheline

alongitsentirelength.Thisisachievedbydrawingperpendicular linesatdesiredinterval (e.g. 20m

to30m) allalongtheroutelength.Thetransversewidth(lengthofcrosssection) oneither sidewill

dependuponthefacilityrequirements.Itis30m to60m for highways,and200m to300m for

railwayson eachsideofthecentreline(Figure11).Thecrosssectionsarethenseriallynumbered,

e.g. CS1, CS2etc. Along eachcross section line, staff intermediate and special stationsare

determined atwhichlevelreadings aretaken andrecorded.Theintermediatestations can be

atan intervalof10meterswhilespecialstations are fixedatallimportantpoints,e.g.pointsofsudden

changeoflevels.Therecordingofreadingsanddrawingthe profileisexactlysimilar to thatof

longitudinalprofiling.



Themapwill thenbeabletosupplyinformationabout

a) Original groundlevel,

b) Formationlevel,

c) Finishedsurfacelevel,

d) Depthofcuttingorfilling,

e) Proposedgradient,and

f)If anyother usefulinformationneededforexecutionoftheconstructionproject.



12.Followingaretheconsecutivereadingstakenwithalevelonacontinuouslyslopingground

atacommonintervalof25m.0.395,1.025,1.795,1.890,2.455,2.880,0.675,1.150,2.425,

0.785, 1.935, 2.465, 2.895.Ruleout apageoflevelfieldbookandmakeentryofabove

readings.Calculatethereducedlevels ofstaffpoints andthegradientofthelinejoiningthe

first and last point.Takethereduced leveloffirst pointas280.00m. (CO1-H1-

AUCMay/June2012)

Solution:


A 0.395 280.000

1.025 0.630 279.370

1.795 0.770 278.600

1.890 0.095 278.505

2.455 0.565 277.940

B 0.675 2.880 0.425 277.515

1.150 0.475 277.040

C 0.785 2.425 1.275 275.765

1.935 1.150 274.615

2.465 0.530 274.085

2.895 0.430 273.655

∑B.S=1.855 ∑F.S=8.200 ∑Rise=0 ∑Fall= 6.345

Check

:

∑B.S–∑F.S=1.855–8.200=-6.345



2

2

∑Rise–

∑Fall =0 –

6.345=-

6.345

LastR.L –FirstR.L= 273.655–280.000=- 6.345

Fall= 6.345

Gradient =

=

Fall

L(N )

6.345

25(13 )

Gradient =0.0231

Slope=1in 43



0

13.Following observationsweretaken in areciprocallevelling:

Instrumentat Staff reading at

A B

A 1.625 2.545

B 0.725 1.405

DeterminetheRLofBifthatofA is100.00mandalsotheangularerrorincollimationifthe

distancebetween Aand B is1000m. (CO1-H1-

AUCMay/June2012) Solution:

i) DetermineRL of B :

Observationtakenfrom A,

DifferenceinelevationbetweenA&B=2.545-1.625

=0.92m(Aishigher)

ObservationtakenfromB,

DifferenceinelevationbetweenA&B=1.405–0.725

=0.68m(Aishigher)

Truedifferenceinelevation=

0.92

2

.68

=0.8m



R.L of B=100

ii) Combined correction for

Correction=0.06728

=0.06728x

=0.06728m

iii) Errorin observation= 0

Error duetocollimation=0

=0

Collimationerror ispositive

tanα=

0.052

7

1000

Buttan60” =0.000290

tan

tan60"


101

0

0–0.8=99.2m

orcurvatureandrefraction:

8d2

8x(1)2

8m (Bislower)

0.92 –0.8=0.12m

0.12–0.06728

0.0527m

e.

.0000527

09

III SEM

surveying I

α=



0.0000527

0.0002909

527x60

2909

α=10.86”= 11”(upwards)



14.Thefollowingstaffreadingswereobservedsuccessivelywithalevel.Theinstrumenthaving

beenmovedafterthesecond,fifthandeighthreadings.0.675,1.230,0.750,2.565,2.225,

1.935,1.835, 3.220,3.115and2.875.thefirststaffreadingwastakenwithastaffheldona

benchmarkofreducedlevel 100.00m.enterthereadingsinthelevel bookformandfindthe

reduced levelsofallpoints. (CO1-H1-

AUCNov/Dec2012)

Solution:

Station B.S I.S F.S H.I R.L

A 0.675 100.675 100.000

B 0.750 1.230 100.195 99.445

2.565 97.630

C 1.935 2.225 99.905 97.970

1.835 98.070

D 3.115 3.220 99.800 96.685

2.875 96.925

∑B.S=6.475 ∑F.S=9.550

Check

:

∑B.S–∑F.S=6.475–9.550=-3.075

LastR.L –FirstR.L= 96.925–100.000=- 3.075

Fall= 3.075



15.Explain thesourcesofvariouserrorsin levelling. (CO1-H1-

AUCNov/Dec2012)

Thesourcesoferrorsinlevellingexercisecanbeseveraldependinguponthelocation,

instrumentemployedandhumanresource.Themajor sourcescanbelistedasfollows

(a) Instrumental errors.

(b) Humanerrorsinsetting.

(c) Natural causes.

a)InstrumentalErrors:

a) Thefocusingtubemaybefaultycausingsometiltinginlineofsightwhilefocusing.

b)Thebubblemaybesluggishorinsensitive.Itcanremainincentral positionevenwhen

bubbletubeisnothorizontal.

c)Morecommonandseriousinstrumentalerrorismaladjustment oflevel.Thebubble tube

lineandcollimationline do notremain parallel.Evenwhen thebubbletubeishorizontal,the

collimationline mayremaininclined.

d) Thestaff graduationsmaynotbeaccurategivingwrongresults.


Civil Engineering Department 105 surveying

I

b)HumanErrors:

Inaccuratelevellingofinstrument bysurveyor whilesettingtheinstrument, or

settlingoflevel duringsurveyingintroduceserrors.Theerror iscumulative.Theerror

canbeavoidedbytakingcare tosetthelevel inafirm groundandlevellingitcarefully.Ifsettingonsoft

groundcannotbeavoided, thelegs ofleveltripodarekeptonwoodenplatformoronstakes

drivenintheground.Thesame

precautioncanbetakenatchangeandintermediatestationstoavoidstaffsettlement. Careshould

betakentoavoidanycontactwithtripodwhilesightingandtakingthestaffreading.Other human

errorscouldbeerrorinfocusingorstaffnotbeingheldperfectlyverticalwhiletakingthe

levelreadings,wrongrecordingofreadingsor recordinginwrongcolumnsetc.

c)NaturalCauses:

Theseareeffectsofwindandsun.Considerabledifficultycouldbeexperiencedwhile

takingthestaffreading underglaringsun, orsunshiningon theobjectiveglass. Accuracyof

observationcan also beaffectedwhen thevelocityofwindislargeorwhenthe atmosphereis

heated.Whenthesightsarelongduringprecisionlevellingtheerrorsduetoeffectofcurvatureand

refractionshall betakeninto account.Thelineoflevel,definedasalineofequalaltitude,willnot

remainhorizontal inlongsightsduetoearth’scurvature(Figure12).Aa′will betherecordedlevel at

AwhilethereallevelshouldbeAa.Thus,anerrore=aa′isintroducedduetoearth’scurvature

givenasec=0.0785D2,whereD isthedistanceinkilometer (km) fromthelevel tothestaffstation,

andeisinmeters.Innormallevelling,sightlengthislessthan300m,henceewillalwaysbeless

than0.007 m.



I

Errorsduetorefractionsareintroducedduetorefractionoflightpassingthroughlayersof

airofdifferent densities.Thebentlightrayfromstafftoinstrumentwillnotremainhorizontal(Figure

13)butwillbecurvedintroducingerroraa′.Theeffectofrefractionisnotconstantbutvarieswith

atmosphericconditions.However,onanaverageundernormal.



atmosphericconditions thecorrectionforrefractionwillbeaa′.Theerror,er(inmeters)=0.0112D2

(i.e. roughly about 1/7 the correction due to curvature and opposite in sign). The

combined correctionduetocurvatureandrefractionwouldbeeCO=eC–er=(0.0785–

0.0112)D2=0.0673

D2.Astheeffectofcurvatureistoincreasethestaffreadingsothecorrectionforcurvatureis

subtractive.Thecorrectionfor refractionisadditivetostaffreading.Hence,thecombinedcorrection

issubtractivetostaffreading.

16.Comparetheriseandfalland lineofcollimation methodsin reducing leveling observation.

(CO1-H1-AUC May/June2013)

Riseand FallMethod:

Insteadoffinding theinstrument heightatasetupstation,thedifferencebetween

consecutivepointsisobtained from theirstaffreadingswiththatimmediately precedingit.The

differenceindicatesariseorafall.Thereducedlevelofeachpointisthenobtainedbyaddingthe

risetoor subtractingthefall from theRLoftheprecedingpoint.Thearithmeticcheckinthismethod

isasfollows:



Σ BS–Σ FS=Σ Rise–ΣFall

= LastRL–FirstRL

Itcanbenoted thatthe firstmethod ofcollimationissimplerand faster than theriseand fall

method.However, thereis nocheckinreductionoflevelsatintermediatestationsincollimation

methodwhilethesecondmethodprovidesarithmeticcheckonallthelevelreductions. Wecan

concludethatthe collimationmethodcan bepreferred forprofilelevellingorsetting

outconstruction levels,whileriseand fallmethodispreferred

fordifferentiallevelling,checklevellingandother importantapplications.

Someprecautionsinrecordingthemeasurementsinfieldbooksshouldbetakentoavoid

errorinrecordingandsubsequentcomputations.Careshouldbetakentomakeentriesstrictlyin

therespectivecolumns prescribedfortheminorderoftheirobservation.Thefirstentryonafresh

pagein fieldbookshall alwaysbeabacksightwhilethelastentryisaforesight.Ifthelastentry

happenstobeastaffpositionatintermediatepoint,insteadofachangepoint,itshall bemadeboth

inforesightandbacksightcolumns atthe endof the preceding page andas thefirstentryintothe

succeeding page. In the remark column, bench marks, change points and other important



informationshallbebrieflybutaccuratelyrecorded,preferablyexplainedwiththehelpofsketches

byfreehanddrawnontheleftsideofthepage.

CollimationMethod:

Asexplainedearlier,theheightofinstrument(HI),e.g.theheightoflineofcollimation

aboveBM(stationofknownlevel)ateachinstrumentstationis determined by

addingthebacksightofBMstationtoreducedlevelofBM.Fromthisheightofinstrumentataparticularinstrum

ent station,reducedlevelsofallthestationpointsongroundarecalculatedbysubtracting foresightof

thatparticular stationfromHI,i.e.

HIofinstrument=RLofBenchmark+BSofBM

RLofintermediatepoint=HI–FSatintermediatestation

=HI–IS

Whentheinstrumentisshiftedtoitssecondposition,heightofinstrument atnewsetup

stationisrequiredtobedetermined.Thisisachievedbycorrelating thelevelsoftwocollimation planes(first

andsecondposition)byforesightofchangepointfrom

firstsetupstationandbacksightofsamechangepointfrom secondsetupstation,asfollows:

RLofchangepointC=RLofA+BSatA–FSatC

HI(atsecondstationO2)=RLofC+BSatC

Withinstrumentsetupatsecondstation(sayO2),staffreadings atnewsystem of

intermediatestationsaretakenbeforeshiftingtheinstrumentatnextsetupstation(O3).This process is

continuously repeated till the levelling exercise is completed,and all the required

reducedlevelsareobtained.



Acheckcan beappliedonthemathematicalcorrectnessofcalculationofreducedlevelsby

collimationmethodasfollows.Thedifferencebetweenthefirstreducedlevel(atstartingstation)

andlastreducedlevel(at endstation)mustbeequaltothedifferencebetweensummationofall

foresightsatchangepointsandthesummationof all backsightsatchangepoints.



UNIT 4

LEVELLING APPLICATIONS

PART A

1. Reduced level of Bench Mark A (CO1-L1-AUC

NOV/DEC 14) - 50.000m Reading on

staff held at A - 2.435m

Reading on staff held at station point B -

1.650m Find: (a) Height of collimation.

(b) Reduced level of station point

B. (c) Rise/fall of B with respect

to A.

(a). Height of collimation = RL of BM A +

BS (HOC) = 50.000 +

2.435

= 52.435m

(b) Reduced level of station point B.

= HOC – FS.

= 52.435 - 1.650



= 50.785 m

( c). Rise/fall of B with respect to A.

= 2.435- 1.65 ( Lower staff reading being higher)

= 0.785m,

= with compare to A, the station point B being 0.785m higher.

2. Compare height of collimation method and rise and fall method.

SI.No Height of collimation method Rise and fall method

1. It is more rapid, less tedious and simpler as it involves few calculation.

It is more laborious and tedious , involving several calculations. 2. There is no check on the RL of

the There is a check on the RL of the

3. Errors in intermediate RL’s cannot be

Errors in intermediate RL’s can be

4. There are two arithmetic checks on

the accuracy of RL calculation.

There are three arithmetic checks

on the accuracy of RL calculation.

5. It is suitable in the case of L.S and

It is suitable in fly leveling where I

3. Write the formula for curvature correction, refraction correction

and combined correction. (CO1-L1-AUC NOV/DEC 14)

Curvature correction CC = 0.07849 d2 ( negative) m



Refraction correction Cr = 0.01121 d2

(positive) m

Combined correction. C = CC – Cr = 0.06728 d2

(negative) m. Note: ‘d’ is to be substituted in Km, while the corrections will be in m.

4. List out the various sources of errors in levelling.

Three principal sources:

(i). Instrumental error

a. Error due to imperfect

adjustment b. Error due to

sluggish bubble.

c. Error due to movement of objective

slide. d. Error due to defective joint.

e. Error due to incorrect length of

staff. (ii). Natural error.

a. Earth’s

curvature.

b. Atmospheric

refraction.

c. Variations in

temperature. d.

Settlement of tripod.

e. Wind

vibrations. (iii). Personal

errors.



a. Mistakes in manipulation. b. Mistake in staff handling

c. Mistake in reading the staff. d. Error’s in sighting.

e. Mistakes in recording.

5. List out the leveling problems. (CO1-L1-AUC NOV/DEC 14)

1. Levelling on Steep Slope.

2. Levelling on Summits and Hollows.

3.Taking Level of an Overhead Point.

4. Levelling Ponds and Lakes too Wide to be Sighted across.

5. Levelling across River.

6. Levelling on Past High Wall.

6. Define sensitivity of a bubble. State any two factors affecting the same.

The sensitiveness of a bubble is defined the angular value of one

division of the bubble tube. It means the capability of showing small angular

movements of the tube vertically. It can be increased by:

1. Increasing the internal radius of the tube.

2. Increasing the diameter of the tube.

3. Increasing the length of the tube.

4. Decreasing the roughness of the walls.



5. Decreasing the viscosity of the liquid.

7. What is a spire test?

It is used to make the horizontal axis perpendicular to the vertical

axis. This test is also known as the test for the adjustments of the standards. It

is done by means of the adjustments of the vertical hair. It is one of the

permanent adjustment of the level and theodolite.

8. Define Contour, contour interval and, horizontal equivalent. (CO1-L1-AUC

NOV/DEC 14)

Contour: A contour is an imaginary line on the ground joining the

points of equal elevation.

Contour interval: It is the vertical distance between any two

consecutive contours. It depends upon the nature of the ground, the scale of

the map and the purpose of the survey.

Horizontal equivalent: It is the horizontal distance between any two

consecutive contours. It varies according to the steepness of the ground.

9. What are the different Characteristics of contour?

1. Contour lines are closed curves. They may either within the map

itself or outside the map depending upon the topography.

2. Uniformly spaced, contour lines indicate a uniform slope.

3. A series of closed contours with increase in elevation from

outside to inside in plan denotes a hill.



4. A series of closed contours with increase in elevation from

inside to outside in plan denotes a depression.

5. The spacing between the contour lines depends upon the slope of

the ground. In steep slopes, the spacing is small and for gentle slope, the

spacing is large.

PART B

1. Describe in detail how would you proceed profile leveling or longitudinal

sectioning in the field. (CO1-H1-AUC MAY/JUNE 2015)

Profile Leveling

Profile leveling is a method of surveying that has been carried out along the central

line of a track of land on which a linear engineering work is to be constructed/ laid.

The operations involved in determining the elevation of ground surface at small spatial

interval along a line is called profile leveling.

Stations



The line along which the profile is to be run is to be marked on the ground before

taking any observation. Stakes are usually set at some regular interval which depends

on the topography, accuracy required, nature of work, scale of plotting etc. It is

usually taken to be 10 meter. The beginning station of profile leveling is termed as

0+00. Points at multiples of 100m from this point are termed as full stations.

Intermediate points are designated as pluses.

Procedure

In carrying out profile leveling, a level is placed at a convenient location (say I1) not

necessarily along the line of observation. The instrument is to be positioned in such a

way that first backsight can be taken clearly on a B.M. Then, observations are taken

at regular intervals (say at 1, 2, 3, 4) along the central line and foresight to a properly

selected turning point (say TP1). The instrument is then re-positioned to some other

convenient location (say I2). After proper adjustment of the instrument, observations

are started from TP1 and then at regular intervals (say at 5, 6 etc) terminating at

another turning point, say TP2 . Staff readings are also taken at salient points where

marked changes in slope occur, such as that at X.

The distance as well as direction of lines are also measured.



Reduction of Level

2. Describe in detail how the

Pegs

Distance(m)

Direction

A

1 0+00

2 0+10

3 0+20

4 0+30

B 0+40

5 0+50

X 0+53.35

6 0+60

7 0+70

8 0+80

9 0+90

C 1+00


119

e cross sectioning done using a leveling

Staff Reading

Difference

in

Elevation

(m)

H.I (m)

R.LB.S I.S F.S Rise Fall

3.005 108.620 105

2.285 0.720 106

1.560 0.725 107

1.785 0.225 106

2.105 0.320 106

2.875 3.105 1.000 108.390 105

3.465 0.590 104

3.955 0.490 104

3.120 0.835 105

3.015 0.105 105

2.580 0.435 105

1.955 0.625 106

1.465 0.490 106

5.880 4.570 3.935 2.625

III SEM

surveying I

Field

book

for

instrument.

R.L(m)

Remarks

105.615 B.M.

106.335

107.060

106.835

106.515

105.515 T.P.1

104.925

104.435

105.270

105.375

105.810

106.435

106.925 T.P.2



Cross Sectioning

In many projects, terrain information transverse to the longitudinal section (through

profile leveling) is also required such as for highways, railways, canals etc. In those

cases, surveying is carried out at right angle to the central line, generally, at regular

interval is being carried out and is termed as cross- sectioning. If, for any reason, a

cross-section is run in any other direction, the angle with the centre line is required to be

noted. The observations are then recorded as being to the left or right of the centre line.

The notes of the readings are maintained as shown in for taking a cross-section along

the stake point 4. Reduction of levels, Plotting etc. can be done as in case of profile

leveling.

right

1.780

106.840

6m

right

B 0+40 2.875 3.105 1.000 108.390 105.515 T.P.1

:

7. Derive the value of curvature and refraction corrections.



Curvature correction:

For long sights , the curvature of the earth affects staff readings . The line of sight is

horizontal , but the level lines is curved and parallel to the mean spheroidal surface

of the earth. the vertical distance between the line of sight and thel level line at a

particular place is called the curvature correction. Due to the curvature objects

appear lower than they really are:



CE6304 SU

It varies with temperature, terrain and other atmospheric conditions. It is

usually considered to be one seventh times but in opposite nature to the error due

to curvature. To minimize this error, reciprocal observation at the same instant of

time is required to be adopted.In actual field condition, the line of

sight through a level is not straight but it bends downward due to the

refraction of rays of light as it passes through the intervening medium.

Cr= 1/7 × (D2/2R)

3. When is reciprocal leveling done? Describe the method along with a

sketch.( CO1-H1-AUC MAY/JUNE 2015)

In the case of an obstacle like river valley, it is not possible to set the up the

level midway between two points on the opposite banks. In such cases the method

of reciprocal leveling is adopted, which involv3es reciprocal observations from

both banks of the river or valley. Two sets of staff readings are taken by holding the

staff on both banks. In this case it is found that the errors are completely eliminated

and the true difference of level is equal to the mean of the two apparent

differences of level. The principle is explained as follows.



up very near a and after proper temporary adjustment , staff readings are

taken at A and B. Suppose the readings are a1 and b1.

2. 2. The level is shifted and set up very near B and after proper adjustment ,

staff readings are taken aat A and B .Suppose the readings are a2 and b2.

Let h = true difference of level between A and B



1. Differentiatebetweenlatitudesa

S.No Latitude

(L) 1.

It maybedefined as itsclength

measuredparallel

2. Thelatitude of thelineisp

measurednorthward (u

is termedasnorthing. 3.

Thelatitude of thelineisn

measuredsouthward(dow

is termedassouthing. 4. L1=L1cosθ1

2. Whatarethe errorseliminated

Errorsduetoeccentricityo

vernierreadings.


121

UNIT 5

THEODOLITE SURVEYING

PART A

esanddepartures. (CO1-L1-AUCApr/May2

e Departure

(D) coordinate It maybedefined as itscoor

measuredat rightangles

tothemeridian direction. spositivewhen

(upward)and

Thedepartureofthelineispo

measuredeastwardand

is termedaseasting. snegative when

ownward)and

Thedepartureofthelineisne

measuredwestwardand

is termedaswesting. D1=L1sinθ1

edinmeasurementofhorizontal anglebymeth

(CO1

A

ofverniersandcentresareeliminatedbytakingb

III SEM

surveying I

ay2011)

rdinate length

ositive when

egative when

hod ofrepetition?

CO1-L1-

AUCApr/May2011)

gboth



Errorsduetoinadjustments

takingbothfacereadings.

Theerrorsdueto inaccurate

partsofthecircle.

Errors duetoinaccurateb

extentcounter-balanced

3. WhatisGale’stable? State

Traversecomputations a

Characteristics:

Thesumofalltheobserved

Ifexterioranglesaremeas


122

ntsoflineofcollimationand thetrunnionaxisaree

s.

ategraduationsare eliminatedbytaking therea

ebisection oftheobject,eccentriccenteringetc.,

cedin differentobservations.

ate its characteristic.

AUCApr/May2010)

ns areusuallydonein atabular formiscalled Gal

edinterioranglesisfoundwhichshouldbeequalto

asuredthenthesumshould beequalto(2n+4) ri

III SEM

surveying I

sareeliminatedby

adingsatdifferent

, maybe tosome

c. (CO1-L1-

le’stable.

o(2n-4)right angle.

ightangles.



Thereducedbearingsofal

lines.

Thelatitude anddepartu

The independentcoord

coordinates.

4. Whatkindoferrorcanbe elimin

Errordueto lineof collimati

axis. Errordueto horizontal

Errordueto non-parallelism

Errordueto imperfect adj

5. Whatismeantbyparallax? Nov/Dec2011)

Parallaxisaconditionarising

thecrosshairs.

6. Name thetemporaryadjustments

Nov/Dec2011)

Setting

Levellingand


123

llthelinesarecomputedbasedonthewholecircl

ure ofall thelinesarecomputed.

dinatesof thelinesareobtainedfromthe corrected co

natedbytaking faceleft andfaceright obse

(CO1-L1-A

ation not beingperpendiculartothehorizontal

al axisnotbeingperpendicular tothevertical a

smof theaxisoftelescopelevel and lineofcollim

justmentof theverticalcircle vernier.

? (CO1

ngwhentheimageformedbytheobjectiveisnot

mentsinatransittheodolite. (CO1-L1-AUC M

III SEM

surveying I

lebearingofthe

ected consecutive

ervations?

AUCApr/May2010)

cal axis.

mation.

CO1-L1-AUC

tintheplaneof

May/June 2012,



Parallaxremoval.

7. Whatistransit theodolite?( CO1

Atransittheodoliteison

180oin thevertical

plane.

8. Whatistheuse of Gale’stable?

Nov/Dec2010)

Thesumoflatitudes(∑L)a

Necessarycorrectionsare done

The independent coordin

coordinates.

Thecoordinatesare posit

9. Whatiscentering ofa theodoli

Theprocessof setting theth


124

CO1-L1-AUC Nov/Dec2010)

neinwhichthelineofsightcanbereversedbyrev

e?

)anddepartures (∑D) arefound.

e done in closedtraverse suchthat∑L= Oand

nates of the lines are obtained from corrected co

tive and theentiretraverselie in thefirstquadra

ite?( CO1-L1-AUC Nov/Dec2009)

heodoliteexactlyoverthestation markisknown as

III SEM

surveying I

volvingthetelescope

e? (CO1-L1-AUC

d ∑D =O.

ected consecutive

drant.

n asCentring.



10.Whatisfacerightobservation?

If thefaceofthe vertical circ

11.Briefhowatheodolitecan be usedasa

Afterhavingcentred andapproximate

of footscrewsand with referenceto

levelsdependsuponwhether three

12.How wouldyou eliminate par

Nov/Dec2012)

Parallaxiseliminatedin two

steps, Focusing

theeyepiece

Focusing theobjective


125

?( CO1-L1-AUC Nov/Dec 2009)

cle is totherightof theobserverisknown asface

n be usedasalevel.( CO1-L1-AUC May/June 20

ately levelledtheinstrument.Accuratelevelling

otheplatelevels.Themanner oflevellingtheins

eelevellingscrewsorfour levellingscrews.

e parallaxintheodolite?

III SEM

surveying I

acerightobservation.

012)

ngisdonewith thehelp

nstrument bytheplate

e? (CO1-L1-AUC



PART–B (16marks)

1. Describe brieflyabouttemporaryand permanentadjustmentsofatheodolite.

(CO1-H1-AUC May/June 2013) TemporaryAdjustments:

i) Setting

ii) Levelling

iii) Parallaxremoval

i) Setting:

Thevertical axisoftheinstrumentshall belocatedexactlyabovethesurveystationposition

markedbyapegpermanentlyfixedinground.Thetopofthepegisnormallymarkedwithacross by

permanentpaint.In normal theodolites,a hookisplacedinthecentreoftripodstand

representingthepositionofverticalaxisoftheinstrument.Aplumbbobissuspendedfromthis hook

with thehelpofa strong thread.

Theinstrumentassembly issetonthefirmgroundandtripodlegsaremanipulatedtobe

approximately overthestationpoint. Thelegsarethenmovedsidewaysand/orradially tobring

plumbbobexactlyoverthe cross junctionon pegwhilemaintainingtribachhorizontal.In more

refined theodolites,opticalplummetisusedforcenteringinplaceofplumbbobassemblyforbetter



accuracy.Acenteringplatemountedontripodcanalsobeused forrapidly centeringthe

instruments.

ii)Levelling:

Toensure thatthehorizontal circledoeslieinatruehorizontal planewhichisnormal to

verticalaxisoftheinstrument,thetheodoliteislevelled.Thisisdonewiththehelpofleveling

screwsand platebubbles.Normally,theinstrumenthas threelevelingscrewsand two

platebubble tubes. Theupperplateoftheinstrumentis rotateduntil one ofthebubble tube is

parallelto theline

joiningtwolevelingscrews.Whilethesecondbubbletubewillbenormaltothisline.Thebubble of

the firsttubeisbroughttocentralpositionbymovingthecorrespondingpairoflevelingscrews

simultaneously.Thethirdscrewisthenmanipulatedtobringbubblesinsecondbubbletube

midwayofitsrun. Thismovementmaycause disturbance in positionoffirstbubble.

Theprocessof levelingisthen iterated untilbubblesofboththe tubes

remainslockedupincentralpositioninall

rotationsofupperhorizontalplate.Thiswillensureperfecthorizontality ofhorizontalcircleand

makesinstrument’svertical axis trulyvertical.



I

iii)ParallaxRemoval:

Itconsistsoffocusingoft

objectlenscoincidethecrosshai

oftheobjectlensandeyepiecesc

tubeuntilthecrosshairsaredist

islockedinfocusedcondition.A

objectandthefocusingscrewis

mayberequiredeverytimethed

observation. Thisensures tha

PermanentAdjustments:

AsexplainedinElement

beidentifiedas:

vertical axis,

axes ofplate levels,

lineofcollimation(alsokn

trunnionaxis (orhorizont

Bubble lineof thealtitude l

Foraninstrument togive

mustexistbetweentheabovefu


128

theeyepieceandobjectlenssothatthefociofthee

airsplane.Asafirststep,apieceofwhitepaperisp

ecescrewismanipulatedtomoveeyepieceinorouto

tinctlyandclearlyobservable.Thisprocessensures

Asanextstep,thetelescopictubeisdirectedtowardsad

sturneduntiltheobject’simageappearssharpan

hedistancebetweentheobjectandinstrumentcha

at theimage ofobjectisformedin theplane of the

tsofSurveying(Unit6),thefundamentalaxesoft

soknown aslineofsight),

tal axisortransverseaxis), and

e level (orazimuthal axis).

ereliableandaccurateobservations,certainde

undamentalaxesoftheinstrument.Theserelati

III SEM

surveying

heeyepieceand

splacedinfront

ofinstruments

suresthateyepiece

ardsadistinct

ndclear. Thisstep

angeswhilemaking

hecrosshairs.

thetheodolitecan

efinitiverelationships

ationshipsmustalso



I

be maintained during theen

arethe properties ofthe instru

Therelationshipswhichm

asfollows:

Theplatelevelsaxisisnorm

Thehorizontal axisisnorm

Lineofcollimation mustbep

Thetelescope’saxismustbep

Inaddition toabovere

requirementstomakethe instru

Theonlymovementofonep

notbe anybacklash,wh

Theverniersofavernierty

vertical circle verniersh


129

ntiresurveyingexercise.It maybenoted that t

umentanddonotchange with surveystationpos

mustexistbetweenfundamentalaxesoftheinstr

rmalto vertical axis.

rmal to vertical axis.

stbeperpendiculartohorizontal axis.

stbeparallel tolineofcollimation.

elations,thewelladjustedtheodoliteshouldalso

umentworkingeasilyand smoothly.

epartrelativetoanothershouldbealongacirculararc.

hip orlooseness.

ypetheodoliteshallbediametricallyoppositetoe

ershould read zerowhen theinstrument islevelle

III SEM

surveying

these relationships

sitions.

rumentcan belisted

someet following

ararc.There should

oeachother.The

ed.



2. Writeshortnotesonbalancingoftraverse.Listoutthedifferentmethodsofbalancinga

traverse.( CO1-H1-AUCApr/May2011)

Thetermbalancingisgenerallyappliedtotheoperationofapplyingcorrectionstolatitudes

anddeparturessothat∑L=0and∑D=0.Thisappliesonlywhenthesurveyformsaclosed polygon.

Thefollowingare commonmethods of adjusting traverse:

i) Bowditch’s method

ii) Transit method

iii) Graphicalmethod

iv) Axis method

i)

Bowditchrule:

Thebasisofthismethodisontheassumptionsthattheerrorsinlinearmeasurements

areproportional to l wherelis thelengthofaline. TheBowditch’s rule is also termedasthe

compassrule.Itismostlyusedtobalanceatraversewherelinearandangularmeasurementsare

equalprecision.Thetotalerrorinlatitudeandinthedepartureisdistributedinproportiontothe

lengthsof

thesides.

Bowditch

Ruleis



Correctiontolatitude (ordeparture)ofanyside

=Total error inlatitude(ordeparture)

X

Thusif CL = Correctiontolatitudeofanyside

CD= Correctiontodepartureofanyside

∑L= total error in latitude

∑D= total errorin departure

∑l= lengthof the perimeter

l= lengthofanyside

Lengthofthatside

perimeteroftravers

e

Wehave CL= ∑Lx

ll

and CD= ∑Dx

ll

ii)TransitMethod:

Thetransit rulemay beemployedwhereangularmeasurements aremoreprecisethatthe

linearmeasurements.Accordingtothisrule,thetotalerrorinlatitudesanddeparturesisdistributed

inproportionto the latitudesanddeparturesof the sides. Itisclaimed that the anglesareless

affectedbycorrectionsappliedbytransit methodthat bythosebyBowditch’s method.


Civil Engineering Department 132

surveying I

The transit ruleis:


= Total error

inlatitude(ordeparture)X

Where L=latitude ofanyline

D=departure of any line

LT=arithmeticsumoflatitudes

DT=arithmeticsumof departure

Latitude(departure)ofthatlin

e

Arithmeticsumoflatitudes(departur

es)

L

Wehave,CL= ∑L x

LT

D

andCD= ∑Dx

DT

iii) Graphical method:

Forroughsurvey,suchasacompasstraverse, theBowditchrulemay beapplied

graphically withoutdoing theoreticalcalculations. According tothegraphicalmethod, it is not

necessarytocalculatelatitudesanddeparturesetc.howeverbeforeplottingthetraversedirectly

fromthefieldnotes,theanglesorbearingsmaybeadjustedtosatisfythegeometricconditionsof

thetraverse.


Civil Engineering Department 133

surveying I

ThepolygonAB’C’D’E’A’representsanunbalancedtraversehavingaclosingerrorequal

toA’AsincethefirstpointAandthelastpointA’arenotcoinciding.The totalclosingerrorAA’is

distributedlinearlytoallthesidesinproportiontotheirlengthbya graphicalconstructionshownin

figure.AB’,B’C’,C’D’etcarerepresent thelengthofthesidesofthe traverseeithertothe same

scaleorreducedscale. TheordinateaA’ismadeequalto theclosingerrorA’A.byconstructing

similartriangles, thecorrespondingerrorsbB’,cC’,dD’,eE’are found.ThelineseE’,dD’,cC’,bB’

respectively. ThepolygonABCDEsoobtainedrepresentsthe adjustedtraverse. It shouldbe

remembered thattheordinatesbB’,cC’,dD’,eE’,aA’representthe correspondingerrorsin

magnitude onlybut not in direction.

iv)AxisMethod:

Thismethodisadoptedwhentheanglesaremeasuredveryaccurately,thecorrections

beingappliedtolengthsonly.Thustheonlydirectionsofthelineareunchangedandthegeneral



I

shapeofthediagramispreserved.Toadjusttheclosingerroraa1 ofatraverseabcdefa1 the

followingprocedureisadopted.

Joina1aandproduceittocutthesidecdinx.thelinea1xisknownastheaxisof

adjustment.Theaxisdivides thetraverseintwo parts i.e. ab c xand a1fed x.

Bisecta1ainA.

Join xb,xe and xf.

ThroughA,draw alineABparalleltoabcuttingxbproducedinB.throughB,draw alineBC

parallelto bccuttingxcproduced inC.

Similarly,through A,draw AF parallel to a1fto cut xfin F.through F,draw FE parallelto

feto cutxe inE. throughE, drawED parallel to edto cutxd inD.

ABCDEF(thicklines)istheadjustedtraverse.


The

image part with relationship ID rId67 was not found i…

The image part with relations

hip ID rId68 was not found i…


The image part with




I

Ax

Now, AB= ab

ax

Correctionto ab= AB –ab=

Axab- ab=

ax

Aaab

ax

=1a1a

2 ax

ab=1

2

ab

xclosingerror

ax

1

Similarly,correction toa1f=

2

a1

aa

1x

1

a1f =

2

a1 f

a1x

xclosingerror

Takingax a1x=length ofaxis.

Weget thegeneralrule:

Correction toany length= that

lengthx

1

x(closingerror/ Lengthofaxis)

2

The image part with relationship ID rId71 was not found in the file.



Theaxisa1x shouldbeso chosenthatitdividesthefigureapproximatelyintotwoequalparts.

Insomecasestheclosingerroraa1may notcutthetraverseormay cutitinveryunequalparts.In

suchcases,theclosingerroristransferredtosomeotherpoint.In figureaa1whenproduceddoes

notcutthe traversein twoparts. Through a,alineae’isdrawnparallelandequal toa1e.throughe’,

alinee’d’isdrawnparallelandequaltoed.Anew unadjustedtraversedcbae’d’isthusobtainedin

which the closing error dd’ cuts the opposite side in x, thus dividing the traverse in two

approximatelyequalparts.Theadjustmentismadewithreferencetotheaxisdx.Thefigure ABCDE

shown bythicklines representstheadjustedfigure.

3. During atheodolite surveythe followingdetailswerenoted:

Line Length(m) Back Bearing

AB 550 60O

BC 1200 115O

CD ? ?

DA 1050 310O



Calculatethelengthand bearingofthelineCD. (CO1-H1-AUCApr/May2011)

Solution:

Line

Latitude Departure

+ - + -

AB 275 476.31

BC 507.14 1087.56

DA 674.92 804.34

Sum 949.92 507.14 1563.87 804.34

∑LI= 442.78 ∑DI= 759.53



LatitudeofCD = - ∑LI =- 442.78m

DepartureofCD= - ∑DI=- 759.53m

Sincelatitude anddepartureofCDisnegative. It lies

inSWquadrant. Thereducedbearing of CD(θ) is

tanθ=

Departur

e

Latitude

759.53

=

442.78

=1.72

θ= tan-1(1.72)

Bearing ofCD, θ = S 58o49’W= 238o49’

LengthofCD=

Latitude

=

cos

442.78

cos(58049

')

=855.15m

Length of CD=855.15m

4. InanopentraverseABCDE,itisrequiredtofindlengthofAEandtofixthemidpointofAE.

Followingistherecordofreadings. (CO1-H1-AUCApr/May2010)



Line Length(m) Bearing

AB 130.5 N20O30’E

BC 215.0 N60O15’E

CD 155.5 N30O30’E

DE 120.0 N30O30’E

i) Determinethelengthand bearingofAE.

ii) AlsodeterminethelengthandbearingoflinejoiningmidpointofAEandthestation

C.

Solution

:

Line

Latitude Departure

+ - + -

AB 122.24 45.70

BC 106.68 186.66

CD 133.98 78.92

DE 103.39 60.90

Sum 466.29 372.18

∑LI= 466.29 ∑DI= 372.18

LatitudeofEA = - ∑LI =- 466.29m

DepartureofEA= - ∑DI=- 372.18m



Sincelatitude anddepartureofEA isnegative. It lies inSWquadrant.

Thereducedbearing of EA(θ) is

tanθ=

Departur

e

Latitude

372.18

=

466.29

=0.798

θ= tan-1(0.798)

Bearing ofEA,θ= S 38o35’W= 218o35’

Length ofEA=

Latitude

=

cos

466.29

cos(38035

')

=596.51 m

Length of EA=596.51m

5. Explainhowtheheight ofatowercan be determinedwhenit isinaccessible.

(CO1-H1-AUCApr/May2010)

Tomeasuretheverticalangleoftowerwithrespecttoinstrumentstationoranyotherpoint.TheI

nstrumentsusedareRanging rods,Theodolite and stand.

TomeasuretheVerticalangle ofanobject A atastation“O”.




Setuptheinstrumentover‘O’and level itwith referencetothealtitude bubble.

Setthe zeroof thevertical vernierexactlyto the zeroof theverticalcircle bymeans of

the vertical circle clampandtangent screw.

Bring thebubble ofthealtitude level tothecenter ofitsrun. The lineofCollimation isthus

made horizontal,while thevernierreadszero.

Loosen the vertical circleclamp,direct thetelescope towardstheobject‘A’,andsighted

approximately,clampthe vertical circle andbisect ‘A’ exactlybyturning

thetangentscrew.

Road both venires.Themean of thetwo,readingsgives thevalueofthe

requiredangle. Changethefaceoftheinstrument andrepeat the process.Themean of

the two vernier

readingsgives thesecond valueof therequiredangle.

Tomeasurethevertical angle between thetwo pointsA andB

Bisect‘A’ as beforeandnotethereadingsonthevertical circle.

Similarly,bisect‘B’ and notethereadingsonthe vertical circle.



The image part with relationship ID rId75

was not found i…



The








Thesumordifferenceofthesereadingsw

illgivethevalueoftheanglebetweenA&B

as one ofthepoints isabove

andtheother belowthehorizontal

plane. Theformula

usedtofindtheheight ofthetoweris h1=

Dtanθ1

h2= Dtanθ2

Heightof total object,H= h1+ h2

R.Loftopof theobject = R.LofB.M+S+h1

R.Lofbottomof theobject = R.LofB.M+ S–h2

Aftertakingthereadingsfindthereducedleveloftopandbottomofthetower.Finallyby using

thereducedlevel find theheightof thetower.




6. Explainhow would youmeasurethedeflection angleusingatheodolite. (CO1-H1-

AUCApr/May2010)

Adeflectionangleistheanglewhichasurveylinemakeswiththeprolongationofthe

preceedingline.Itisdesignatedasright(R)ofleft(L)accordingasitismeasuredtotheclockwise

oranti-clockwisefromtheprolongationofthepreviousline.Itsvaluemayvaryfrom0oto180o.the

deflection angle atQ isαoR andthat at R isθ°L.

Tomeasurethedeflection angles at

Q:

i)Set theinstrumentat Q and level it.

ii)With bothplatesclampedat 0°, take backsightonP.

iii)Plungethetelescope.Thusthelineofsightisin thedirectionPQ producedwhen thereadingon

vernierAis0°.

iv)Unclamp theupper clampandturnthetelescopeclockwise to taketheforesight

onR.Readboth theverniers.

v)Unclampthelowerclampandturnthetelescope tosight P again. Readboththeverniers.



Plungethetelescope.

vi)Unclamp theupper clampandturnthetelescope tosight R. read bothverniers.Sincethe

deflectionangle is doubledbytakingbothfacereadings, one-halfof thefinal readinggives

the deflectionangle at Q.



7. ItisnotpossibletomeasurethelengthandfixthedirectionofalineABdirectlyonaccount

ofanobstructionbetweenthestationsAandB.AtraverseACDBwasthereforerunand

following datawasobtained.

Line Length(m) ReducedBearing

AC 45 N 50OE

CD 66 S 70OE

DB 60 S 30OE

Findthelengthand directionof line BA. (CO1-H1-AUC Nov/Dec2011)

Solution:

Line

Latitude Departure

+ - + -

AC 28.92 34.47

CD 22.57 62.02

DB 51.96 30

Sum 28.92 74.53 126.49

∑LI= - 45.61 ∑DI= 126.49

LatitudeofBA = ∑LI =45.61m

DepartureofBA= - ∑DI=-126.49m

Sincelatitude ofBA ispositive and departure ofBA isnegative. It lies inNWquadrant.



Thereducedbearing of BA (θ) is

tanθ=

Departur

e

Latitude

126.49

=

45.61

=2.77

θ= tan-1(2.77)

Bearing ofBA,θ= N70o9’W= 289o51’

Length ofBA=

Latitude

=

cos

45.61

cos(7009'

)

=134.32 m

Length of BA=134.32 m

8. Explainthe variousmethods ofhorizontal angle using atheodolite.

(CO1-H1-AUC Nov/Dec2011

There aretwo methodstofindthehorizontal angle

usingatheodolite.Theyare i) Repetition Method

ii) ReiterationMethod



I

RepetitionMethod

:

Tomeasure ahorizontal angle byrepetition

method.Theinstrumentsusedare

Transit theodolite,

Tripodand

Ranging rods(2no.s).

Procedure:

Setuptheinstrumentover‘O’ and level itaccurately.

Withthehelp of upper clampandtangent screw, set0º readingonvernier‘A’.Notethe

readingofvernier‘B’.

Release theupper clampand direct thetelescopeapproximatelytowardsthepoint‘P’.

Tightenthelowerclampandbisect point‘P’ accuratelybylowertangent screw.

Release theupper clampandturntheinstrument clock-wise towardsQ.Clamptheupper

clampandbisect ‘Q’ accuratelywith theupper tangentscrew.Notethereadingsofverniers

‘A’ and ‘B’ toget thevaluesoftheangle POQ.

The image

part with relationship ID rId83 was not found i…



The


The image part with relationship ID rId87 was not

found i…



found i…



I

Release thelowerclampandturnthetelescope clockwise to sightP again.Bisect P

by using thelowertangent screw.

Release theupper clamp, turnthetelescopeclockwise and sight Q.Bisect Qbyusing

the upper tangent screw.

Repeattheprocessuntiltheanglemeasured(requirednumberof timesis3).Theaverage

angle withfaceleftwill be equal tofinalreadingdivided bythree.

Changefaceandmakethreemorerepetitionsasdescribed above.Findthe averageangle

withfaceright,bydividing thefinal readingbythree.

Theaveragehorizontal angle isthenobtained bytaking theaverageofthetwo angles with

faceleft andfaceright.

Aftertaking thereadingscalculatethehorizontal angle andhorizontal distancebyusing

the formula. Thenwefindthe exacthorizontal angleand thedistancebetween thepoints PQ.


The



The image





ReiterationMethod

:

Tomeasureahorizontal angle

byreiterationmethod.Theinstrumentsusedare

Transit theodolite,

Tripodand


Procedure:

It is requiredtomeasureangles AOB, BOC,andCOD etcbyreiteration method.

Settheinstrument over“O” and level itset theVernierto zeroandbisectpointA accurately.

Loose theupper clampand turntheTelescopeclockwise topointB.BisectB byusing the

upper tangent screw.

Read boththeVerniers, the meanoftheVerniers will give theangles AOB.

Similarly,bisectsuccessively C,D etc, thusclosing thecircle. Read boththe

Verniersat each bisection.

The image




The



found i…


The image part with relationship ID

rId101 was not found i…




Finallysight toAthereadingof theverniershould bethesameastheoriginal setting

reading.

Repeatthe steps02to04 with otherfacei.e. faceRight.

Aftertaking thereadingsthen calculatethehorizontal anglefor each points.

9. Describethe essential parts ofa transit theodolite. (CO1-H1-AUC

Nov/Dec2009) EssentialParts:

Leveling head, telescope, vertical circle, index frame, A frame, lower plate, upper

plate,level tubes,plumbbob.

Leveling Head:-

Thelevelingheadconsistsoftwoparalleltriangularplanesknownastribrachplates.

Theuppertribrachhasthreearms,eachcarryingalevelingscrew. Thelowertribrachhas

threearms eachcarryingalevelingscrew. Thelowertribrachplateorfootplatehasacircular

holethrough which plumb bobmaybesuspended.

Telescope:-

Thetelescopeisanintegralpartofthetheodoliteandismountedonaspindleknown

ashorizontal axisortrunnionaxis. Inmostof thetransits, internalfocusingtelescopeisused.




I

Vertical Circle:-

The vertical axis is a circular graduated arc attached to the trunnionaxis of the

telescopeconsequentlythe graduatedarcratherwiththetelescopewhenthelatteristurned

aboutthe horizontalaxis.

IndexFrame:-

The indexframeisaT-shapedframeconsistingofaverticallegknownasclippingarm

andahorizontalbarknownasvernierarmofindexcorm.Atthetwoextremitiesoftheindex

armarefittedtwo verniers toreadthevertical circle.

AFrame:-

TwostandardsresemblingtheletterAaremountedontheupperplates. Thetrunnion

axisofthetelescope issupported onthese.

Lower Plate:-

Thelowerplateisattachedtotheouterspindle.Thelowerplatecarriesahorizontal

circleat itslevelededgeandisthereforealsoknownas thescale plate.

Upper Plate:-

Theupperplateorvernierplateisattachedtotheinneraxisandcarriestwovernierswith

magnifiers at two extremities diametrically opposite.Theupper plate supports the

standards.

PlumbBob:-

Aplumbbobissuspendedfromthehookfittedtothebottomoftheinneraxistocentre

ofinstrumentexactlyoverthestation mark.



I

Telescope:

It consistsofeye-piece,objectglass andfocusingscrewand it isused tosight theobject.

Verticalcircle:

It isusedtomeasurevertical angles.

Footscrews:

These are usedto leveltheinstrument.



10.Explainthetheodoliteadjustmentforthelineofsight. (CO1-H1-AUC

May/June 2012)

Ifthelineofsightisnotperpendiculartothetrunnionaxisofthe telescope,itwillnotrevolve in

aplane when the telescope is raisedorloweredbutinstead,itwill traceoutthesurfaceofacone.

Thetraceoftheintersectionoftheconical surfacewith thevertical planecontainingthepointwill be

hyperbolic.Thiswillcauseerrorin the measurementofhorizontalangle betweenthepointswhich

areatconsiderable difference inelevation.



Intheabovefigure,letPandQbetwopointsatdifferentelevationandletP1 andQ1 be

theirprojectionsonahorizontaltrace.LetthelineAPbeinclinedatanangleα1 tohorizontalline

AP1.Whenthe telescope isloweredaftersightingPthehyperbolictracewillcutthehorizontaltrace

P1Q1inP2iftheintersectionofthecross-hairsis totheleftoftheoptical axis.Thehorizontalangle

thusmeasuredwillbewith respectofAP2andnotwith respecttoAP1. Theerror‘e’ introducedwill

thusbee= βsecα1,whereβ istheerrorinthe collimation.

Onchangingthe face,however,theintersectionofthecross-hairswillbetotherightofthe

opticalaxisandthehyperbolictracewillintersectthelineP1Q1 inP3.Thehorizontalanglethus

measuredwillbetherespecttoAP3,theerrorbeinge=βsecα1 totheotherside.Itisevident,

therefore,thatby takingboth faceobservationstheerrorcanbeeliminated.AtQalso,theerrorwill

bee’=βsecα2,whereα2istheinclinationsofAQwithhorizontalandtheerrorcanbeeliminated by

takingboth faceobservations.Ifhowever,only one faceobservations aretaken toPand Q, the

residualerrorwillbeequaltoβ(secα1 -secα2)andwillbezerowhenboththepointsareatthe

sameelevation.



11.List themethods ofcheckingin anopentraverseandclosedtraverse. (CO1-H1-AUC

May/June 2012) Checks inOpenTraverse:

Nodirectcheckofangularmeasurementisavailable.However,indirectcheckscanbemade

as shown inbelowfigures.



Infigure(a),inadditiontotheobservationofbearingofABatstationA,bearingofADcan

alsobemeasured,ifpossible.Similarly,atD,bearingofDAcanbe measuredandcheckapplied.If

thetwobearingsdifferby 180o,thework(uptoD)may beacceptedascorrect.Ifthereissmall

discrepancy,it canbeadjustedbeforeproceedingfurther.

Anothermethod,whichfurnishesacheckwhentheworkisplottedisasshowninfigure(b)

andconsistsinreadingthebearingstoanyprominentpointPfromeachoftheconsecutive

stations.ThecheckinplottingconsistsinlayingoffthelinesAP,BP,CP,etc.and nothingwhether

thelinespass throughonepoint.

Incaseoflongandprecise traverse,the angularerrorscanbe determinedby astronomical

observationsforbearingat regularintervalsduring theprogressofthetraverse.

Checks in closedTraverse:

Theerrors involved intraversing aretwokinds:linearand angular. Forimportantwork

the most satisfactorymethodofchecking thelinearmeasurementsconsists

inchainingeachsurvey linea secondtime,preferably in thereversedirectionondifferent

datesand bydifferent parties. Thefollowingarethechecksfortheangularwork.

1)Traversebyincluded angles:

a) Thesumof measuredinteriorangles shouldbeequalto(2N-4) right angles,where N=

numberofsidesofthetraverse.

b) Iftheexterior angles aremeasured, theirsumshouldbeequalto(2N +4) right angles.

2)Traversebydeflection angles:



Thealgebraicsumof thedeflectionanglesshould beequalto 360o,taking theright-

hand deflection angles aspositive and left-handanglesas negative.

3)Traverse bydirect observation ofbearings:

Theforebearingofthelastlineshould beequalto itsbackbearing+ 180omeasuredat the

initial station.

12.ThemeasuredlengthsandbearingsofthesidesofaclosedtraverseABCDEruninanti-

clockwisedirectionaretabulatedbelow.CalculatethelengthofCDandDE.

(CO1-H1-AUC May/June 2012)



I

Solution:

Line

Latitude Departure

+ - + -

AB 298.7 0

BC 186.12 87.58

EA 173.52 124.23

Sum 658.92 124.23 87.58

∑LI= 658.92 ∑DI= 36.65

LatitudeofCE = - ∑LI =- 658.92m

DepartureofCE= - ∑DI=- 36.65m

SincelatitudeanddepartureofCE isnegative. It lies

inSWquadrant. Thereducedbearing of CE(θ) is

tanθ=

Departur

e

Latitude

36.65

=

658.92

=0.056

θ= tan-1(0.056)

Bearing ofCE, θ = S3o12’ W=183o12’

Length

ofCE=

Latitude

=

cos



I

658.92

cos(3012')

=659.95

m

Length of CE=659.95 m

Angle DCE = α =75o6’

Angle CDE = β=

48o30’ Angle DEC = γ

= 56o24’



DE

sin

CE

=

sin

DC

=

sin

DE

sin7506'

DE

sin7506'

659.95

=

sin48030'

659.95

=

sin48030'

DC

=

sin56024'

DE=851.53m

DC 659.95

=

sin56024'

sin48030'

DC = 733.94m

13.FromthefollowingdataofaclosedtraversePQRS.Calculatethelengthandbearingofthe

lineSP. (CO1-H1-AUC Nov/Dec2012)

Line Length(m) WCB

PQ 85 N 83O36’E

QR 137 N 42O15’E

RS 67 N 63O18’W



Solution:

Line

Latitude Departure

+ - + -

PQ 9.47 84.47

QR 101.41 92.11

RS 30.10 59.85

Sum 140.98 176.58 59.85

∑LI= 140.98 ∑DI= 116.73

LatitudeofSP = - ∑LI =- 140.98m

DepartureofSP= - ∑DI=-116.73m

Sincelatitude anddepartureofSP isnegative. It lies inSWquadrant.

Thereducedbearing of SP (θ) is

tanθ=

Departur

e

Latitude

116.73

=

140.98

=0.827

θ= tan-1(0.827)



Bearing ofSP, θ = S 39o35’W= 219o35’

Length ofSP=

Latitude

=

cos

140.98

cos(39035

')

=182.92 m

Length of SP=182.92 m

14.Explaintheanglemeasuring proceduresusingtheodolite. (CO1-H1-AUC

May/June 2013)

Theinstrumentsusedtomeasuretheangles are Transit theodolite,Tripodand


Thefollowingproceduresareusedtofindtheangles,

Setuptheinstrumentover‘O’and level itaccurately.

Withthehelp of upper clampandtangent screw, set0º readingonvernier‘A’.Notethe

readingofvernier‘B’.

Release theupper clampand direct thetelescopeapproximatelytowardsthepoint‘P’.

Tightenthelowerclampand bisect point‘P’ accuratelybylowertangent screw.




The image part with




Release theupper clampandturntheinstrument clock-wise towardsQ.Clamptheupper

clampandbisect ‘Q’ accuratelywith theupper tangentscrew.Notethereadingsofverniers

‘A’ and ‘B’ toget thevaluesoftheangle POQ.

Release thelowerclampandturnthetelescope clockwise to sightP again.Bisect P

by using thelowertangent screw.

Release theupper clamp, turnthetelescopeclockwise and sight Q.Bisect Qbyusing

the upper tangent screw.

Repeattheprocessuntiltheangle measured(requirednumberof timesis3).Theaverage

angle withfaceleftwill be equal tofinalreadingdivided bythree.

Changefaceandmakethreemorerepetitionsasdescribed above.Findthe averageangle

withfaceright,bydividing thefinal readingbythree.

Theaveragehorizontal angle isthenobtained bytakingtheaverageofthetwo angles with

faceleft andfaceright.


The image










15.ExplainBowditchrulewith example. (CO1-H1-AUC

May/June 2013)

The basisofthis method ison the assumptions that the errorsin linear measurementsare

proportionalto l where listhelengthofaline.TheBowditch’sruleisalsotermedasthe

compassrule.Itismostlyusedtobalanceatraversewherelinearandangularmeasurementsare

equalprecision.Thetotalerrorinlatitudeandinthedepartureisdistributedinproportiontothe

lengthsof thesides.

Bowditch Ruleis


=Total error inlatitude(ordeparture)X

Thusif CL = Correctiontolatitudeofanyside

CD= Correctiontodepartureofanyside

∑L= total error in latitude

∑D= total errorin departure

∑l= lengthof the perimeter

l= lengthofanyside

Lengthofthatside

perimeteroftravers

e

S.K.P. Engineering College, Tiruvannamalai III SEM

Civil Engineering Department 166 Surveying I

skp engineering college -...

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