CE6304 Surve Unit 3-5

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UNIT –III

LEVELLING AND APPLICATIONS :

Level line – Horizontal line – Levels and staves – Spirit Level – Sensitiveness

– Bench marks – Temporary and permanent adjustments – Fly and check leveling –

Booking – Reduction – Curvature and reraction – Reciprocal leveling – Longitudinal

and cross sections – !lotting – Calculation o areas and volumes – cantering –

methods – characteristics and uses o contour"s plotting# $arth %ork volume –

capacity o reservoirs

leveling

Levelling is a &ranch o surveying the o&ject o %hich is '

()* to ind the elevations o given points %ith respect to a given or assumed

datum+

(,* to esta&lish points at a given elevation or at dierent elevations %ith respect to

a given or assumed datum#

Level Line - level line is a line lying in a level surace# .t is+ thereore+ normal to

the plum& line at all points#

Horizontal Line .t is straight line tangential to the level line at a point# .t is alsoperpendicular to the line deined &y a plum& line#

principle o! levelling

The principle o level lies in urnishing a horizontal line o sight and ind the

vertical distance o the points a&ove or &elo% the line o site# - line o sight is

provided %ith a level+ and a graduated leveling sta provides the vertical height o

a station %ith reerence to the level line#

Intr"#ent $eig$t%The elevation o line o site %ith respect to assumed datum is kno%n as height o

instrument or instrument height# .t does not mean the height o telescope a&ove the

ground level %ere the level is setup#

te#porar& a'("t#ent o! a level%

Temporary adjustments are done &eore the &eginning o the survey and ater

each shiting o the instrument#

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(i* Centering o &u&&le to align the line o sight horizontal using oot scre%s#

This should &e checked oten since slight distur&ance o the instrument aects the line

o sight to a large e/tent#

(ii* Focusing o telescope to a distant o&ject

(iii* -djustment o eye piece to have a clear vie% o the cross hairs

c$ange point

The point at %hich &oth a ore sight and &ack sight are taken during the

operation o levelling is called a change point# Sights are taken rom t%o dierent

instrument station a ore sight ascertains the elevation o point to esta&lish the height

o instrument at the ne% instrument station# The change point is al%ays selected on a

relatively permanent point#

reciprocal leveling

0hen it is necessary to carry levelling across a river+ ravine or any 1&stacle

re2uiring a long sight &et%een t%o points sosituated that no place or the level can &e

ound rom %hich the lengths o oresight and &ack sight %ill &e even appro/imately

e2ual+ special method that is reciprocal

levelling must &e used

• Let - and B &e the points and o&servations &e made %ith a level+ the line o

sight o %hich is inclined up%ards %hen the Bu&&le is in centre o its run#

• The level is set at a point near - and sta reading are taken on - and B %ith

the &u&&le in the centre o its run#

• Since B#3# - is very near to instrument+ error due tocurvature+ reraction and

collimation %ill &e introduced in the sta readings at -#But there %ill &e an

error e in the sta reading on B#


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• The level is then shited to the other &ank+ on a point very near B#3# B+ and

the readings are taken on sta held at B and -#

• Since B is very near+ there %ill &e no error due to the three actors in reading

the sta+ &ut the sta reading on - %ill have an error e#

• Let ha and h& &e the corresponding sta readings on - and B or the irst set

o the level and ha" and h&" &e the readings or the second set#

A lig$t $o"e i ("t vii)le !ro# *+ ,# in ea% -in' t$e $eig$t o! t$e lig$t $o"e%

4istance d 5 678m

Height o light house 5 h

0e kno%+ h 5 7#79:; / d< 5 )9=#,6m

Na#e t$e o"rce o! error in leveling%

$rrors in leveling may &e categorized into

(i* !ersonal error

(ii* $rrors due to natural actors and

(iii* .nstrumental error

Intr"#ent Ue' -or Levelling

The instrument commonly used in direct levelling are'

()* - level

(,* - levelling sta#

.% LEVEL

- Level consists o the ollo%ing our parts'

) - telescope to provide line o sight

)# - level tu&e to make the line o sight horizontal

,# - levelling head (tri&rach and trivet stage* to &ring the

;# Bu&&le in its centre o run

># - tripod to support the instrument#

T&pe o! level

)#4umpy level ,% 0ye level ;#Reversi&le level >%Tilting level

D"#p& level

)# The dumpy level consists o a telescope tu&e irmly secured in t%o collars

i/ed &y scre%s to the stage carried &y the vertical spindle#


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,# The modern orm o dumpy level has the telescope tu&e and the vertical

spindle cast in one piece and a long &u&&le tu&e is attached to the top o the

telescope# This orm is kno%n as solid dumpy#

Follo%ing are the parts o the dumpy level'

)# T$L$SC1!$ ,# $@$A!.$C$ ;# R-@ SH-4$ ># 1B$CT.$ $D4

6# L1DE.T4.D-L BBBL$ 9# F11T SCR$0S :# !!$R !-R-LL$L !L-T$

=# 4.-!HR-E3 -4ST.DE SCR$0S )7# BBBL$ TB$ -4ST.DE

SCR$0S ))# TR-DS$RS$ BBBL$ TB$

• .n some o the instruments+ a clamp Scre% is provided to control the

movement o the spindle a&out the vertical a/is#

• For small or precise movement+ a slo% motion scre% (or tangent scre%* is alsoprovided#

• The levelling head generally con o t%o parallel plates %ith either threeAoot

scre%s#

• The upper plate is kno%n as tri &ranch and the lo%er plate is kno%n as trivet

%hich can &e scre%ed on to a tripod#

The advantages o the dumpy level over the 0ye level are'

(i* Simpler construction %ith e%er mova&le parts#(ii* Fe%er adjustments to &e made#

(iii* Longer Lie o the adjustments

/&e Level

• The essential dierence &et%een the dumpy level and the 0ye level is that in+ the

ormer case the telescope is i/ed to the spindle %hile in the 0ye levelG the

telescope is carried in t%o vertical 0ye" supports


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• The 0ye support consists o curved clips# . the clips ate raised the telescope can

&e rotated in the 0yes+ or removed and turned end or end# 0hen the clips are

astened+ the telescope is held rom turning a&out its a/is &y a lug on one o the

clips#

• The &u&&le tu&e may &e attached either to the telescope or to the stage carrying

the %yes

• .n the ormer case+ the &u&&le tu&e must &e o reversi&le type# Fig# sho%s the

essential eatures o @Alevel# The levelling head may &e similar to that o a dumpy

level#

• .n some cases+ the instrument is itted %ith a clamp and ine motion tangent or

controlled movement in the horizontal plane#

• The 0ye level has an advantage over the dumpy the act that the adjustments can

&e tested %ith greater rap and ease#

0everi)le Level

• - reversi&le level com&ines the eatures o &oth the dumpy level and the 0ye

level#

• The telescope is supported &y t%o rigid sockets into %hich the telescope can &e

introduced rom either end and then i/ed in position &y a scre%#

• The sockets are rigidly connected to the spindle through a stage#

• 1nce the telescope is pushed into the sockets and the scre% is tightened+ the level

acts as a dumpy level#

• For testing and making the adjustments+ the scre% is slackened and the telescope

can &e taken out and reversed end or end# The telescope can also &e turned %ithin

the socket a&out the longitudinal a/is#


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Tilting Level

• .n the case o a dumpy level and a 0ye level+ the line o sight is perpendicular

to the vertical a/is#

• 1nce the instrument is levelled+ the line o sight &ecomes horizontal and the

vertical a/is &ecomes truly vertical+ provided the instrument is in adjustment#

Follo%ing are the parts o the tilting level'

)# Telescope ,# $yeA!iece ;# Ray Shade ># 1&jective $nd 6# Level Tu&e 9# Focusing

Scre%s :# Foot Scre%s =# Tri&ranch I# 4iaphragm -djusting Scre%s

)7# Bu&&le Tu&e Fi/ing Scre%s ))# Tiltiing Scre%s

),# Spring Loaded !lunger );# Trivet Stage

• .n the case o tilting level+ ho%ever+ the line o sight can &e tilted slightly %ithout

tilting the vertical a/is#

• Thus+ the line o sight and the vertical a/is need not &e e/actly perpendicular to

each other#

• The instrument is levelled roughly &y the threeAoot scre%s %ith respect either to

the &u&&le tu&e or to a small circular &u&&le#

• 0hile taking the sight to a sta+ the line o sight is made e/actly horizontal &y

centering the &u&&le &y means o a ine pitched tilting scre% %hich tilts the

telescope %ith respect to the vertical a/is#

• .t is+ ho%ever+ essential that the o&server should have the vie% o the &u&&le tu&e

%hile sighting the sta# Fig sho%s the essential eatures o a tilting level#

LEVELLING STA--


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• - levelling sta is a straight rectangular rod having graduations+ the oot o the

sta representing zero reading#

• The purpose o a level is to esta&lish a horizontal line o sight#

• The purpose o the levelling sta is to determine the amount &y %hich the station

is a&ove or &elo% the line o sight#

• Levelling staves may &e divided into t%o classes

()* SelAreading sta (,* Target sta#

SEL-10EADING STA--

There are usually three orms o selAreading sta'

(a* Solid sta

(&* Folding sta

(c* Telescopic sta (Sop %ith pattern*#


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Fig (a* and (&* sho% the patterns o a solid sta in $nglish units %hile (c* and (d *

sho% that in metric unit#

.n must common orms+ the smallest division is o 7#7) t# or

The a&ove ig# sho%s a sop%ith pattern sta arranged in three telescopic lengths#

0hen ully e/tended+ it is usually o )#> t (or 6 m* length# The )> t# sta has

solid top length o >" 9J sliding into the central &o/ o >" 9J length#

The central &o/+ in turn+ slides into lo%er &o/ o 6" length# .n the 6 m sta+ the

three corresponding lengths are usually )#6m+ )#6 m and , m#

The a&ove ig sho%s a olding sta usually )7 t long having a hinge at the

middle o its length# 0hen not in use+ the rod can &e olded a&out the hinge so that

it &ecomes convenient to carry it rom one place to the other#

The hundredths o eet are indicated &y alternate %hite and &lack spaces+ the

top o a &lack space indicating odd hundredths and top o a %hite space indicating

even hundredths#


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Target Sta!!

Fig#sho%s a target sta having a sliding target e2uipped %ith vernier# The rod

consists o t%o sliding lengths+ the lo%er one o appro/# : t and the upper one o

9 t#

The rod is graduated in eet+ tenths and hundredths+ and the vernier o the target

ena&les the readings to &e taken up to a thousandth part o a oot#

For readings &elo% : t the target is slided to the lo%er part %hile or readings

a&ove that+ the target is i/ed to the : t mark o the upper length#

For taking the reading+ the level man directs the sta man to raise or lo%er the

target till it is &isected &y the line o sight#

The sta holder then clamps the target and takes the reading K the pper part o

the sta is graduated rom the top do%n%ards#

te#porar& a'("t#ent o! a level

$ach surveying instrument needs t%o types o adjustments

()* temporary adjustments+ and (,* permanent adjustments#

The temporary adjustments or a level consist the ollo%ing'

()* Setting up the level (,* Levelling up (;* $limination o paralla/#

Setting Up t$e Level#

The operation includes

(a* i/ing the instrument on the stand+

(&* levelling the instrument appro/imately &y leg adjustment#


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positions#

Do% rotate the instrument through )=7 degree# The &u&&le should remain in the

centre o its run+ provided it is in correct adjustment#

-o"r Scre2 Hea'

Turn the upper plate until the longitudinal a/is o the ! ate level is roughly parallel

to the line joining t%o diagonally 1pposite Scre%s such as 4 and B Fig#(a*

Bring the &u&&le central e/actly in the same manner as descri&ed in step (,* a&ove

Turn the upper part through I7 until the spirit level a/is is parallel to the other

t%o diagonally opposite scre%s such as - and C as in ig (&* Centre the &u&&le as

&eore#Repeat the a&ove steps till the &u&&le is central in &oth the positions#

Turn through )=7 to check the permanent adjustment as or three scre%

instrument#

proce o! levelling

3i4 INST0U5ENT STATION:1

- point %here instrument is set up or o&servations is called instrument station#

3ii4 HEIGHT O- INST0U5ENT 3Hi4

The elevation o line o site %ith respect to assumed datum is kno%n as height o

instrument#

.t does not mean the height o telescope a&ove the ground level %ere the level is

setup#

6AC7 SITE:1 36S4

- irst site taken on a level sta held at position o kno%n elevation is called

&ack site# .t ascertains the amount &y %hich the line o sight is a&ove or &elo% the

elevation o the point# Back site ena&le the surveyor to o&tain the height o

instrument#


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-O0E SITE:1

The site on a level sta held at a point o unkno%n elevation to ascertain &y

%hat e/tent the point is a&ove or &elo% the line o site is called ore site# Fore site

ena&les surveyor to o&tain the elevation o the point#

CHANGE POINT:1

The point at %hich &oth a ore sight and &ack sight are taken during the

operation o levelling is called a change point# Sights are taken rom t%o dierent

instrument station a ore sight ascertains the elevation o point to esta&lish the height

o instrument at the ne% instrument station# The change point is al%ays selected on a

relatively permanent point#INTE05EDIATE SIGHT:1

The F#S taken on a level sta held at points &et%een t%o turning points

to determine the elevation o points is kno%n as intermediate sight# .t may &e noted

that or one setting o the level there %ill &e only a &ack sight and ore sight &ut there

can &e a num&er o intermediate sights#

A !ollo2ing rea'ing are ta,en 2it$ t$e level 2it$ a 8# leveling ta!! on a

contin"o"l& lope gro"n' at 9+# interval%

7#9=7+ )#>66+ )#=66+ ,#;;7+ ,#=66

;#;=7+ )#766+ )#=97+ ,#,96+ ;#6>7

7#=;6+ 7#I>6+ )#6;7 K ,#,67


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The R#L o starting point %as =7#:67m rule out a page o level &ook an enter a&ove

readings carry out reduction o height &y collimation method and apply arithmetic

checks# 4etermine gradient o the line joining )st and last point#

Station B#S .#S F#S H#C R#L

- 7#9=7 =)#>;7 =7#:67

B )#>66 =)#>;7 :I#I:6

C )#=66 =)#>;7 :I#6:6

4 ,#;;7 =)#>;7 :I#)77

$ ,#=66 =)#>;7 :=#6:6

F )#766 ;#;=7 =)#>;7 :=#767

E )#=97 :I#)76 ::#,>6

H ,#,96 :I#)76 :9#=>7

. 7#=;6 ;#6>7 :I#)76 :6#696

7#I>6 :9#>77 :6#>668 )#6;7 :9#>77 :>#=:7

L ,#,67 :9#>77 :>#)67

S3 ,#6:7 I#):7

-rithmetic check

∑ BS A∑ FS 5 RL o last point – RL o irst point

,#6:7 – I#):7 5 :>#)67 – =7#:67 5 A 9#977

Eradient is 9#977m in ;97m

slope 5 ) in 6>#6>

reciprocal leveling it proce'"re

0eciprocal Levelling:1

- method o dierential leveling is &ased on the act the instrument kept

e2uidistant rom the &ack and or%ard station+ The dierence in elevation o t%o

stations is e2ual to the dierence o the sta readings#

By setting the level mid%ay the error due to the curvature and reraction and

also the collimation error is eliminated# 0hen it is not possi&le


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to set up the level mid%ay &et%een t%o points as in the case o leveling across large

%ater &odies the reciprocal leveling is employed to carry or%ard a levels on the other

side o the o&struction#

P0OCEDU0E:1

(&) – a)* M (&, – a,*

h 5 AAAAAAAAAAAAAAAAAAAAAAAAAAAAA m ,

H 5 4ierents in elevation#

Let - K B &e t%o points on opposite &anks o the lake the dierents o level

o - K B may &e determine as ollo%s'

(i* Set up the level very near to - 8eeping the &u&&le o the level tu&e

centre +take reading on the sta held at - K B#

(ii* Let the sta readings are - K B &e a) and &)#Readings as - is usually

taken through the o&jective as a ield o vie% is very small# - pencil

may &e pointed on the sta till it is see through the telescope a connect

reading is noted#

(iii* Transer instrument to B and set it very near to B %hen the &u&&le is

centered o&serve the readings at - K B as a, and &,#

- true dierence in elevation &et%een - K B is e2ual to the mean o the t%o

apparent dierences o levels#

4ierence in elevation &et%een - and B is

(&) – a)* M (&, M a,*

h 5 AAAAAAAAAAAAAAAAAAAAAAAAAAAAA

,

c"rvat"re correction

CU0VATU0E CO00ECTION: 1 CC 5 7#7:=6d<


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- line o sight is the straight line -ssumed to &e ree rom eect o curvature

a level live is a curve line having its concave surace to%ards the earth# 4ue to

curvature o the earth reading taken on a leveling sta held vertically is al%ays more

than %hat these %ould have &een i the earth has a plan surace#

CU0VATU0E

BC is the departure rom the level line# -ctually the sta reading should have

&een taken at B %here the level line cuts the sta+ &ut since the level provides only the

horizontal line o sight (in the a&sence o reraction*+ the sta reading is taken at the

point C#

Thus+ the apparent sta reading is more and+ thereore+ the o&ject appears to

&e lo%er than it really is the correction or curvature is+ thereore+ negative as applied

to the sta reading K numerical value &eing e2ual to the amount BC#

To ind BC the value BC+ %e have

d<

CC 5 AAAA R 5 9;:7 km,R

5 ;>;<

AAAAAAAAAAAAAAAAAA , / 9;:7777

5 7#77I,; m CC 5 7#:=6 / d<

re!raction correction

0E-0ACTION

The eect o reraction is the same as i the line o sight %as curved

do%n%ard+ or concave +to%ards earth" s surace and hence the rod reading is

decreased# Thereore+ the eect o reraction is to make the o&jects appear high than

they really are#

The correctionG as applied to sta readings is positive#


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The reraction curve is irregular &ecause o varying atmospheric conditions+

&ut or average conditions it is assumed to have a diameter a&out seven times that o

the earth#

The correction o reraction

'itance o! vii)le $orizon i calc"late'%

4.ST-DC$ 1F TH$ .S.BL$ H1R.N1D'A

Let C &e the sta station and B+C &e the sta readings d &e the distance

&et%een the instrument station and sta station# -ssume the horizon meets the earth

surace at the station -#

h 5 7#79:; d<

d 5 √ h O 7#79: m

d is horizon distance

T2o o)ervation 2$ere #a'e !ro# a intr"#ent tation A To a ta!! rea'ing at

6 at a 'itance o! ;*+# !ro# A an' to C 'itance o! 8=6m

d<

CR 5 AAAAAA 5 7#7)), d<

)>R

5 7#7)), / 7#>=6< 5 7#77,9 m


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cc 5 7#7:=6 / 7#>=6< 5 7#7)=6m

True sta value 5 o&served value – CC M CR

5 )#:)6 – 7#7)=6 M 7#77,9

5 )#:m

d< 5 7#,67 km

CR 5 7#7)), d< 5 7#777:

CC 5 7#7:=6 d< 5 7#77>Im

True sta real 5 ;#6,6 – 7#77>I M 7#777:

5 ;#6, m

4ierent elevation real

5 ;#6,7 – )#:77

5 )#=, m

point c is at a higher elevation o )#=, rom B#

longit"'inal ectioning cro ection level can )e plotte'%

LONGITUDINAL SECTIONING

!R1C$4R$

)# !roile levelling+ like dierential levelling+ re2uires the esta&lishment o turning

points on %hich &oth &ack and oresights are taken#

,# .n addition+ any num&er o intermediate sights may &e o&tained on points alongthe line rom each set up o the instrument

;# .t is generally &est to set up the level to one side o the proile line to avoid too

short sights on the points near the instrument#

># For each set up+ intermediate sights should &e taken ater the oresight on the ne/t

turning station has &een taken#

6# The level is then set up in an advanced position and a &ack sight is taken on that

turning point#

9# The position o the intermediate points on the proile are simultaneously located

&y chaining a along the proile and noting their distances rom the point o

commencement#

:# %hen the vertical proile o the ground is regular or gradually curving+ levels are

taken on points at e2ualAdistances apart and generally at intervals o a chain

length#


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PLOTTING O- C0OSS SECTION:1

C0OSS SECTIONING

)# Cross sections are run at right angles to the longitudinal proile and o either side o

it or the purpose o lateral outline o the ground Surace#

,# They provide the data or estimating 2uantities o earth %ork and or other

purposes#

;# The crossAsections are num&ered consecutively rom the commencement o the

centre line and are set out at right angles to the main line o section %ith the chain

and tape+ the crossAsta or the optical s2uare and the distances are measured let

and right rom the centre peg# CrossAsection &e taken at each chain#

># The length o crossAsection depends the nature o %ork#

Plotting t$e pro!ile


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t$e error t$at co"l' creep in leveling an' 2a& to #ini#ize it%

E00O0S IN LEVELLING 'A

$rrors in leveling may &e categorized into

)# !ersonal error

,# $rrors due to natural actors

;# .nstrumental error

PE0SONAL E00O0:1

!ersonal error include the ollo%ing

3i4 Error in ig$ting:

This is caused %hen it is diicult to see the e/act coincide o the crosshairs and the

sta graduation# This may &e either due to long sights or due to poor ocusing o thecrosshair# Some times atmospheric air+ atmospheric condition also cause on error in

sighting# This error is accidental and may &e classiied as compensative#

3ii4 Error in #anip"lation:1

This is due to careless setting up o the level neither the telescope nor

the tripod should &e distur&ed %hile taking readings# The instrument should &e set up

on a irm ground and careully leveled#

Take care that the &u&&le is centre %hen the readings are o&served# .

the &u&&le is not centered a Horizontal a/is telescope gets inclined aecting the sta

readings# The error is more or long sights K less or short sights# To avoid the error

the o&server should develop the ha&it o checking the &u&&le &eore and ater taking

reading#

3iii4 Non Verticall& o! ta!! :


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. the sta is not held vertical during o&servation o the sta reading the

o&served value %ill &e higher than the actual value# The sta should &e held vertical

using a plum& &o

Error i rea'ing t$e ta!! :

These error generally committed are

(i* reading the sta up side do%n#

(ii* Reading top or &ottom hair instead o center hair#

(iii* concentrating the attention on decimal part o reading and entering the

%hole value %rongly#

(iv* reading the inverted sta as a vertically held sta#

Error i recor'ing co#p"tation :1

Common errors is recording are

(i* $ntering the reading in the %rong column that is B#S reading in the .#S or F#Scolumn#

(ii* recording the reading %ith digits inter change#

(iii* 1mitting on entry#

(iv* -dding the F#S reading instead o su&tracting %ith and su&tracting a B#S reading

instead o adding#

Error '"e to nat"ral ca"e :13i4 Error '"e to c"rvat"re :1

The curvature o the earth surace lo%ers the elevation o the station

and it is directly proportional to the s2uare o the horizontal distance &et%een the

sta position and the point o o&servation# The correction o the curvature has to &e

su&tracted rom the o&serve sta reading to get correct reading# .n case o ordinary

leveling error due to curvature in negligi&le that is only 7#77;m or a sight o ;77 m

length#


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3ii4 Error '"e to re!raction :1

The eect o reraction on the o&serve readings is opposite to that o

the curvature# Reraction rise the elevation o the station on the error is also

proessional to the s2uare o the horizontal distance o the station rom the level# This

is negligi&le or short sites and it"s generally ignored in ordinary leveling#

3iii4 Error '"e to 2in' "n :1

4ue to strong %inds it is al%ays diicult to hold the sta vertical due

to non verticality o the sta the o&served reading are higher#The %ind is also

responsi&le or small distur&ance in the instrument level# .n strong %inds it"s al%ays

advisa&le to suspend the %ork#

The sun causes a considera&le trou&le# .t"s recommended to protect the

o&jective &y an um&rella# The eect o sun in also causes elongation o the sta due

to increased temperature &ut in ordinary leveling the changing in length is negligi&le#

Intr"#ental error :1

3i4 I#per!ect a'("t#ent o! level'A .n a perected adjusted level a line o

collimation remains horizontal %hen the &u&&le o the level tu&e occupies the central

position# 0hen adjustment is not perect the line o collimation is either inclined

up%ards or do%n%ards and o&served reading are either more a less# Such errors gets

compensative# . the B#S K F#S distance are kept e2ual as in the case o the leveling#But in the case o inter mediate site the distance reading are thro%n into error &y a

dierent amount# .ncase o leveling an steep slopes#

3ii4 De!ecting level t")e :1 . the &u&&le o level tu&e is sluggish# .t %ill

remain centre even i the &u&&le a/is is not horizontal or on the other hand i its t%o

sensitive a reasona&le time is spent to &ring a &u&&le centre# .rregularly o curvature

o the tu&e is also a series deect#

The eect o delective level tu&e also gets neutralized i the sights are o

e2ual length#

S$a,& tri po' :1

- shaky tri pod consumes a lot o time to center the &u&&le and alters the

instrument setting oten causing the line o sight to veer rom horizontal#

Incorrect gra'"ation o! ta!! :

. graduation o sta are not perect there %ill &e a error during o&servation

&ut in ordinary leveling the error may &e negligi&le &ecause the readings are generally


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graduated in 7#776m incase o precise leveling the graduation should &e compared

against a invar tape#

T$e !ollo2ing cone>"ent rea'ing 2$ere ta,en in a level an' a 8# leveling ta!!

on a contin"o"l& loping gro"n' at co##on interval o! 9+# t$e rea'ing are

+%

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:# - contour line must close upon itsel+ though not necessarily %ithin the limits o the

map#

=# Contour lines cross a %atershed or ridge line at right angles# They orm curves o

Ashape round it %ith the concave side o the curve to%ards the higher ground

I# Contour lines cross a valley line at right angles# They orm sharp curves o Ashape

across it %ith conve/ side o the curve to%ards the higher ground . there is a stream+

the contour on either side+ turning upstream+ may disappear in coincidence %ith the

edge o the stream and cross underneath the %ater surace#

)7# The same contour appears on either sides o a ridge or valley+ or the highest

horizontal plane that intersects the ridge must cut it on &oth sides# The same is true o

the lo%er horizontal plane that cuts a valley#


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#et$o' o! conto"ring

5et$o' o! conto"ring

)# 4irect method

,# .ndirect method

Direct #et$o':

The ield %ork is o t%oAold

ertical control

Horizontal control

Vertical control

• The points on the contours are traced either %ith the help o a level and sta or

%ith a help o a hand level#

• The sta is kept on the B#3# and the height o the instrument is determined#

• Calculate the sta reading For e/ample i height o the instrument is )7)#=m

• means the sta reading %ill &e )#=7m

• Taking one contour at a time the sta man is directed to keep the sta on the point

on contour so that readings o )#=7m are o&tained every time#

Horizontal control

• -ter having located the points on various contours+ they are to &e surveyed %ith a

survey control system#

• For small area chain survey may &e used and points may &e located &y osets#

• .n a %ork o a larger nature a traverse may &e used#

In'irect #et$o'

The ollo%ing are some o the indirect methods'

By s2uare

By crossAsection

By tacheometric method

6& >"are

• The method is used %hen the area to &e surveyed is small and the ground is not

very much undulating#

• The area is divided into a num&er o s2uares#

• The size o the s2uare may vary rom 6 to ,7 m depending upon the nature o the

contour and contour interval#


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• The elevations o the corners o the s2uare are then determined &y means o a

level and a sta#

• The contour lines may then &e dra%n &y interpolation# .t is not necessary that the

s2uares may &e o+ the same size#

• Sometimes+ rectangles are also used in place o s2uares# 0hen there are

apprecia&le &reaks in the surace &et%een corners+ guide points in addition to

those at corners may also &e used#

• The s2uares should &e as long as practica&le+ yet small enough to conorm to the

ine2ualities o the ground and to the accuracy re2uired# The method is also kno%n

as spot leveillng.

6& Cro Section

• .n this method+ crossAsections are run transverse to the centre line o a road+

rail%ay or canal etc#

• The method is most suita&le or rail%ay route surveys#

• The crossAsections should &e more closely spaced %here the contours curve

a&ruptly+ as in ravines or on spurs#

• The crossAsection and the points can then &e plotted and the elevation o each

point is marked#

• The contour lines are interpolated on the assumption that there is uniorm slope

&et%een t%o points on t%o adjacent contours#

• Thus+ the points marked %ith dots are the points actually surveyed in the ield

%hile the points marked %ith / on the irst crossAsection are the points interpolated

on contours#


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6& tac$eo#etric #et$o'

• .n the case o hilly terrain the tacheometric method may &e used %ith advantage#

• - tacheometer is a theodolite itted %ith stadia diaphragm so that sta readings

against all the three hairs may &e taken#

• The sta intercept s is then o&tained &y taking the dierence &et%een the readings

against the top and &ottom %ires#

• The line o sight can make any inclination %ith the horizontal the range o

instrument o&servations#

• The horizontal distances need not &e measured since the tacheometer provides

&oth horizontal as %ell as vertical control# Thus i it is the inclination o the line o

sight %ith horizontal the horizontal distance (4* &et%een the instrument a/is and

the point in %hich the line o sight against the central %ire intersects the sta are

given &y'

4 5 8)s cos, M 8, cos,

5 4 tan

8) K 8, are instrumental constants#


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IV. THEODOLITE SURVEYING :

Theodolite – vernier and micro tic – Description and uses – Temporary

and permanent adjustment of vernier transite – Horizontal angles – Vertical angle

height of distance – Traversing closing error and distribution – cale’s table –

orient measurement.

TACHOMETRY SURVEY :-

Tachometry is a branch of angular surveying in which A horizontal &

vertical distance is of points are obtain by optical means as suppose to ordinary

slow process of measure by tape chain. This methods is very rapid & convenient.

All though the accuracy of tachometry is low it is best adopted in obstructed such

as steep & broken ground stretches of water etc which make drawn age difficult.

They primary object of tachometry is the preparation of contour maps are plans

required with both horizontal & vertical measurements also accuracy

improvement it provides at check an distance measure with tape.

At the instruments a normally transit theodalite pitted with stadia

diaphragm is generally used for tachometry survey. A stadia diaphragm



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essen a y cons s o one s a a a r a ove on e o er an equa s ance e ow

the horizontal cross hair. Telescope is used in stadia surveying are of 3 types :-

(i) Simple external focusing telescope

(ii) External focusing analytic

(iii) Internal focusing telescope

Different system of Tachometry measurements :-

(i) Fixed hair method (or) stadia method(ii) Movable hair method (or) substance

Fixed hair method :-

In method observation are made with stadia diaphragm having stadia

wires at fixed (a) constant distance occur. They reading an the staff

corresponding to all three wires are taken. The staff intercept that is the differents

of reading corresponding to top & bottom stadia wires will depend on the

distance of the staff from the instrument when the staff intercept is more than thelength of the staff only ½ interne of real. For inclined said reading may be taken

by keeping the staff either vertical a normal to the line of site.

Subtense method :-

This method is similar to fixed hair method except the stadia internal is

varying table arrangement is may to --- distance between the stadia hair so as to

said them against the two targets on the staff kept at a point and observation this

in this case the staff intercept that is the distance between the two forgets is kept

fixed while the stadia interval that is the distance between the stadia hair is

carrying as is the case of fixed hair method inclined site they out show be taken

the tangential method. They stadia being taken against the horizontal hair as

against any two point on the staff on their corresponding vertical angles are

measured. This measurement of vertical angles tube for one single observation.

Staff in theodalite normal mean by perpendicular. Least count of staff 0.005m.



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e s a ver ca :-

Horizontal D = MS cos²θ + cos θ

Vertical V = MS sin²θ / 2 + C sin θ

H = height of instruct

R = observe staff reading

S = staff intercept

This is top – bottom hair radia

O = angle made by line of site with horizontal

Reduced level of θ = R.L of p + h-v-r

RL of p + h + v – r = RL of O

Staff normal to lined site :

Find the elevation & horizontal distance of point Q view from A is than

angle of 30° above horizontal with staff intercept with staff held vertically occur

3.855 m & C.H reading 1.930 m elevation of point A is 10m above m.s.l take

multiplying as 100 assume h to be 1 m

RL of A = 10.000 m

RL of Q = RL of A + height of instrument + v – r

V = MS sin²θ / 2 + c sinθ

= 100 x 3.855 sin²30° / 2

= 48.19m

reduce level of Q = 10.000 + 1.000 + 48.190 – 1.930

= 57.260m

Horizontal distance :

D = MS cos²θ + cosθ

= 100 x 3.855 cos²30° / 2

reduce level Q= 57.260m



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. n ver ca or zon a s ance e ween po n . e ns rumen

located 0.8m above A clip of 22° to a staff held normal to the line of site at B. The

staff read 1.650, 2.150, 2.650

Assume m = 100

RL of θ = RL of A + h – v- r cosθ

S = 1m

R = 2.150 r cosθ = 1.993

V = (ms + c) sinθ

= (100 x 1) sin 22° = 37.461m

RL of θ = 0 + 0.8 – 37.461 – 1.993

= 38.654m

horizontal distance D

D = (ms + c) cosθ + r sinθ

= (100) cos 22° + 0.805

D = 93.51m

3. To determine distance between two points with base of one point is axiable

and instrument station in the same vertical plane as the elevated object.

d tan²θ D = -------------------

tanθ1 – tan θ2

h = D tanθ1

Instrument with two different Axis :-

(d + s cot θ2 ) tanθ2D = ---------------------------

tanθ1 – tan θ2

(d + s cot θ2 ) sinθ1 sinθ2h = -----------------------------------

sin (θ1 – θ2 )

h2 = h1 + s



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use pos ve s gn w s co 2 w en ns rumen a axs a s ower nega ve

sign when it’s height the instrument axis at P.

1. An instrument was setup at station P and the angle of elevated to an objective

was 9°30’ the same object was focus from a point 4m away the first one angle

was 11° 150’ the staff reading s from a B.M having elevation 2650.38m are

1.310m and 1.815m respectively. Find the RL of Q = θ1 = 9°30’ θ2 = 11°15’

(d - s cot θ2 ) tanθ2D = ---------------------------

tanθ1 – tan θ2

( 4 – 0.535 ( d 9°30’) tan 9°30’ 0.164 = ----------------------------------------- = ----------

tan 11°15’ – tan 9°30’ 0.0315

D = 5.21m = -204.13m

(4 – 0.505 x 5.98) sin 11°15’ sin 9°30’h2 = ---------------------------------------------------

sin (11°15’ – 9°30’ )= 39.68m

- 49 -

h2 = h1 + s = 39.68 + 0.505

= 39.175

RL of stadia = R.L of D² + S²

= 2650.38 + 1.310 – 39.175

= 2612.52m

2. An instrument was setup a P and the angle of elevation to a volume 4m above

the focus of the staff held at Q was 9°30’. A horizontal distance Pl was know

2000m determine the RL of staff station Q given RL of instrument axis was

2650.38m

0.0673 d²

0.0673 x 2000²

Ccr = 0.673 x 2



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= . m

V = D tanθ

= 2000 x tan 9°30’ = 334.69m

RL of Q = RL of instrument axis + Ccr + V – h

= 2650.38 + 0.27 + 334.69 – 4

= 2981.34m

3. A instrument was setup a P and angle of depression to a plane 2m above the

fast of the staff held at Q was 5° 36’ H. d between P & Q was 3000m determine

RL of staff station Q given the staff readings as a B.M of elevation 436.050m

was 2.865m

Cn = 0.0673 x 3² = 0.6057

V = 3000 x tan 5°36’ = 294.15m

RL of Q = BM + cn – V – n + instrument

= 436.050 + 2.865 – 0.6057 – 294.15= 142.16m

Measurement of horizontal angles :-

(i) Direct method

(ii) Method of Repetition

(iii) Method of Reiteration

Precaution to be taken theodalite observation :-

(i) Turn the theodalite by the standards and not by using telescopeensuring slow & smooth movement.

(ii) Done force the foot screws & tangent screws to heart.

(iii) Clamp vertical axis tightly while observing the horizontal angles.

Sources of errors in theodalite :-

(i) Instrumental Error

(ii) Personal Error

(iii) National Error



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A horizontal angle was measured by repetition with transit 8 times at initial

readings 0°0000 utter first observation reading was 30°25’20’’ & final

measurement was 243°22’10’’ find the angle measured angle 243°22’10’’

Station Ver A Va D

A L 0° 05° 000 0 05’ 30’

R 180’ 00’ 40’ 05’ 20’

B L 50° 55’ 00’ 55’ 20’’

R 230 55 40 55’ 20’’

C L 120 34 20 34 20

R 300 34 00 34 40

D L 210 24 40 24 40

R 30 24 20 24 00

Station Ver A Ver B mean ver aenrol mea Angle

A L 0 05 20 05’ 30’ 5’ 25’ 0°5’27.5” 50°49’52.5”

R 180 05 40 05’ 20’ 5’30’

B L 50 55 00 55’ 20” 55’ 10” 50°55’20’

R 230 55 40 55’ 20” 55’ 30”C L 120 34 20 34 20 34’20” 120°34’20” 69°39°

R 300 34 00 34 40 34’20”

D L 210 24 40 24 40 24’40” 210°24’25” 89°50°5”

R 30 24 20 24 00 24’ 10”

L 360 05 0 05 30 5’25’ 360°5’27.5 49°41°25A

R 180 00 40 05 20 5’30”

360° 0’0”



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Station Ver A Ver B mean ver aenrol mea Angle

A L 0° 01’ 0” 1’ 20” 1’ 10” 0° 01’20” 20°20’5”

R 180° 01’20” 1’40” 01’30”

B L 20°21’20” 21’20” 21’20” 20°21’25” 81°25°30”

R 200°21’40” 21’20” 21’30”

C L 101°47’30” 47’20” 47’20” 101°46°55” 258°42’25”

R 281°46’40” 46’20” 46’30”

A L 860°01°00” 0°01’20” 01’10” 360°01’20”

R 180°01’20” 01°01’40” 01’30”

360° 0’0”



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V. ENGINEERING SURVEYING :

Reconnaissance preliminary and location surveying for engineering

projects – lay out setting out work, Route survey for highway’s railway and water

way curve ranging – Horizontal and vertical curves – syrup’s curves – setting with

chain and tapes, tangential and by theodolite, double theodolite – compound and

curves – Transition curves – Function and requirements setting outs by offsets

and angles – vertical curves – sight distance – mine surveying instruments –

Tunnels – correct of under ground and surface surveys – shorts Adits.

RECONISSONCE SURVEY:-

Preliminary survey:-

(i) Work minimize

(ii) Error minimize

TYPES OF INSTRUMENTING:-

- Tachometry



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- arome ers s ng eve ng e g a e

- sextants (approximate height level)

This is using vertical angle

CURVES:-

Curves are generally used on highways and railways way there is

necessary to change direction of motion. It curve classified as

(1) simple curve

(2) compound curve

(3) reverse curve

Uniform radiations curvature is called simple curve.

Two variable radius curvatures are called the compound curve.

Two curves in upside and downside curve is called reverse curve.

OTHER TYPES:-

Vertical and horizontal curves

BACK TANGENT:-

The tangent AT1 previous to the curve is called Back tangent or first

tangent.

FORWARD TANGENT:-

The tangent T2B following the curve is called second tangent.

POINT OF INTERSECTION:-

If the two tangent AT2 and BT2 are produced they two meet in a point v

called the point of intersection.

POINT OF CURVE:-

It is the beginning of curve where the alignment changes from tangent to

curve.



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POINT OF TANGENCY:-

It is the end of the curve when the alignment changes from curve too

tangent.

INTERSECTION ANGLE:-

The angle between tangent AB, BB is intersection angle at external

deflection angle.

DEFLECTION ANGLE TO ANY POINT:-

The deflection angle to any point on the curve the angle BC between the

back tangent or they move from BC to the point on the curve.

TANGENT DISTANCE:-

It is the distance between PC to PI then be equal to PI & PT

EXTERNAL DISTANCE:-

It is the distance from the mid point of the curve 2PI.

LENGTH OF CURVE: L

It is the total length of curve from PC to (P.T)

LONG CHORD:-

It is a chord joining from PC to PT.

MID ORDINATE:-

It is the ordinate from midpoint of the long chord to the midpoint of the

curve.

NORMAL CHORD:-



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c or e ween wo success ve regu ar s a ons on a curve s ca e

normal chord.

SUB CHORD:-

Sub chord is any chord shorter than normal chord.

RIGHT HAND CURVE:-

If the curve is deflective to the right of the direction of progress of survey iscalled right hand curve.

LEFT HAND CURVE:-

If the curve is deflective to the left of the direction of progress of survey is

called left hand curve.

DESIGNATION OF THE CURVE:-

The sharpness of the curve is designated either by radius at by its degreeof curvature. The degree of curvature is defined as the central angle of the curve

then it subtended by curve 100 ft length. According to the chord definition the

degree of curvature is defined as the central angle of the curve that is subtended

by a chord of 100 feet length.

SETTING OUT OF SIMPLE CURVES:-

(i) LINEAR METHOD:-

In linear method only a chain or tape is used. These used when the

degree of accuracy required is low are when the curve is short.

(ii) ANGULAR METHOD:-

In angular method instrument such as theodolite are used along which

chain or tape. It is hardly accumulated and can be used for longer curves.

Before a curve is set out it is a tangent point of intersection. Point of curve

and point of tangent.



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LOCATION OF TANGENT:-

Before setting out the curve the surveyer is always sub lying with the

working plane upon which the general alignment of tangent is known in relation

of the transverse controlling the survey of the area.

Know in objects to certain points on both a tangents the tangents can be

marked in the ground by tape measure the tangents may be the set out by

theodolite by trivalent error sudden the pass through the mark as really as

possible. The total deflection angle (α) and then it is measured by setting

theodolite on P.I

LINEAR MEASUREMENTS OF SETTING AT CURVES:-

(i) By ordinates or offset by chart.

(ii) By successive bisection of areas.

(iii) By offset from the tangents.

(iv) By offset from the chords.

ANGULAR METHODS:-

(i) Rankine’s method of tangential angle (or) deflection angles.

(ii) Two thedolite method

Rankine’s method:-

∫= 1718.9 C/R minute

(i) Thedolite setting on p.c view in P.I or U in setting o°. calculate (c)

value.

(ii) Turn in 5° to view using ranging rod coordinate point taken.

(iii) Same form by P.T distance



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:-

Set the thedolite point curve T1 with both clamp to zero.

Direct the thedolite to by sec the point of inter section (v)

The line of site is tube in the direction of the rear tangent.

release the vernear plate and set angle D an the veneer

The line of site is direct alloy T10

with the zero an end of the tape potted T1 and an arrow held at a distanceT1A = C

Suring the tape around T1 the arrow is by section by the cross hair thus

the first point a is fixed set the second defection angle ∆2 : 2∆1 on the

vernear so that the line of site is directed along T1B

With the zero end of tape pinot at A and an arrow held at an distance AB =

C sue the tape arrow A till the arrow is by sected by the cross hairs thus

fixing they point B

Repeat the last two steps till the point T2 is reached.

The last point show located must coin side with the point of tangent T2 if

the deviation is small last tube may be adjusted. If it’s more the whole

curve should be resected.

Incase of left hand curve each of calculated values of defection angle D

should be subtracted them 360° the show obtained are to be set on they

vernear of the theodalite

Procedure :-

(i) set up one theodalite at T1 with a zero reading facing the point V (P.i)

similarly setup another theodalite at T2 (P.T) with zero reading facing T1

(P.C) set the reading of each of transit to the defection angle S1 for the first

point A. The line of site of both the theodalites are thus directed towards A

along T1A & T2A respectively.



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move a rang ng ro n suc a way a y sec s syman ous y e

cross hairs of both instrument thus point A is fixed. To fix the second point B

set readings S2 cm both instruments an by sects the ranging rod repeat the

last two steps for location of remaining points.

The method is expansion since two instruments & two surveyor are

required. How ever the methods is more accrue since each point is fixed

independently of the other.

Lenear method of setting out curves:

(i) By ordinate from long chord

L = length of long chord

R = Radius of curvature of the curve

To set out the curve a long chord is divided into even number of equal

points offsets are calamite from formula & then set out a each of these points.

(ii) By successive by section of arcs or chords:-

CD = R (1 – cos ∆ /2)

EF = R ( 1- cos ∆ /4)

GH = R (1 –cos ∆ /8)

Joint the tangent T1, T2 & by sect the long chord D, erected DC &

make in equal to R (1 – cos ∆ /2)

Joint T1C & T2C by sect them a F & F1 at F1 and F2 set out offsets

equal to R (1 – cos ∆ /4) to get the point EE1 on the curve by

successive by section of these chords more points can be obtain

offset from tangents.

Setting out compound curve :-



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s curve may e y e me o o e ec on ang es. s ranc s

set out by setting theodalite T1 and second branch is setout by set the at the

point D.

(i) For the first curve calculate the tangent angles for set out curve by

rankines method.

Set the theodalite at T1 & set out the first branch of curve calculating the

chord length C.

Calculate the tangent angles for second branch and set out curve by

placing instrument at D mark the curve T2 is reach.

(ii) Set the observation by measure angle T1 D1 T2 with should be equal

to

∠ T1 DT2 = 180 – (∆1 + ∆2 /2 )

Transverse Curve :

Transitional curve : Starting point -> radius of curve.

General requirement of T.C :

(i) A T.C is easement curve is the curve of varing radius introduce

between a straight line under circular curve are between two branches of the

compound or reverse curve.

In case of high way in orded to whole the vehicle in the entry of the la. The

drive is required to move his steering almost insentaniously to the position of



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CE6304 Surve Unit 3-5