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ENGINEERING SURVEY 2 C 2005 / 1 /

Article I.

Article II.

0

MODULE

MALAYSIAN

POLYTECHNICS

MINISTRY OF EDUCATION

UNIT 1UNIT 1


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TACHYMETRY

OBJECTIVES

General Objective : To know and understand the bas! !on!e"ts o# dstan!e

$easure$ent%

Specific Objectives : &t the end o# the unt 'ou shou(d be ab(e to :)

E*"(an the bas! !on!e"ts o# +"t!a( ,stan!e

-easure$ent%

,s!uss the s'ste$ that has been use n ta!h'$etr'%

Ca(!u(ate the dstan!e b' usn. the ta!h'$etr' s'ste$%

E*"(an the "ro!edure to $"(e$ent the #e(d work

E*"(an the ste"s to "ro!ess the obseraton data%

st errors n ta!h'$etr' sure'%

1

UNIT 1


3/48


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(en.th o# ths base% I# the base (en.th and "ara(a!t! an.(es are known9 then the (en.th o#

the "er"end!u(ar bse!tor !an be !a(!u(ated% 34.ure 1%2

4.ure 1%2 Isos!e(es Tran.(e Geo$etr'3Sour!e : Ukur 6 ? 3Cd * Cot @/2

I# dstan!e &> 6 ,9 dstan!e Cd 6 S 9 so

Ahereb'

, 6 dstan!e between two "ont

S 6 base (ne@ 6 "ara(a!t! an.(e

#.( TACHYMETRY SYSTEM

The a(ternates o# the ta!h'$etr' s'ste$ are !(ass#ed based on the bas!

"rn!"(es9 wh!h are:

a 4*ed an.(e:

1 The stada s'ste$

In!(ne S.hts Ath The Sta## Vert!a(

B

, 6 ? S Cot @/2


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In!(ne S.hts Ath The Sta## Nor$a(

b Varab(e an.(e

1 tan.enta( s'ste$ ert!a( sta##

2 subten!e s'ste$ horDonta( sta##

The theodo(te s a standard nstru$ent n ea!h !ase% It s $od#ed to sut the !ondtons%

#.(.# T)e Sta*ia S+ste,

The da"hra.$ n ths s'ste$ !ontans two addtona( horDonta( (nes known as

stada hars% It s "(a!ed eudstant aboe and be(ow the $an horDonta( !ross har

34.ure 1%B% The dstan!e between these stada har s !a((ed the stada ntera( 34.ure

1%1% Ths stada ntera( s usua((' a !onstant9 "rodn. #*ed)har ta!h'$etr'% Ths

ntera( $a' be a(tered on so$e nstru$ents and the $oe$ent ben. $easured on a$!ro$eter%

4.ure 1%B The Vew In The Te(es!o"e

3Sour!e: Ukur


6/48


#.(.#.# T)e Sta*ia '-r,la

The stada $ethod o# "rodn. the horDonta( dstan!e between nstru$ent andsta## s shown n 4.ure 1%F% Ths te!hnue s a(wa's used n stada ta!h'$etr' #or

en.neern. sure'% The te(es!o"e !onssts o# two !entrn. tubes% The e'e"e!e and

da"hra.$ are bu(t at the end o# tube% -oe the ob=e!t .(ass wh!h s bu(t at the other

sde when don. #o!usn.%

Ahen the te(es!o"e s n #o!us9 the $a.e o# the sta## &> w(( be #or$ed at abn

the "(ane o# the da"hra.$% Then a ra' o# (.ht w(( e$er.e "ara((e( to the o"t!a( a*s

s$(ar(' wth the ra' #ro$ > as shown% The ra's here w(( #or$ two s$(ar tran.(es

ea!h wth ther a"e* at 49 the base o# the s$a((er tran.(e at the ob=e!t .(ass ben. eua( tothe stada ntera( i%

E'e"e!e

,a"hra.$

Vert!a(a*s

!ket

4.ure 1%F Stada rn!"(e

3Sour!e and Sure'n.9 Ra$sa' H%% A(son

f))) the #o!a( (en.th o# the ob=e!t .(ass

4 the outer #o!a( "ont o# the ob=e!t .(assi))) the stada ntera( ab

I))) the dstan!e #ro$ the outer #o!a( "ont to the sta##

,)))the horDonta( dstan!e reured

s))) the sta## nter!e"t &>

!)))the dstan!e #ro$ ob=e!t .(ass to nstru$ent a*s

5


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4ro$ these s$(ar tran.(es:

i

f

s

l=

but l6 D (f + c),

So9 the stada #or$u(a:i

f

s

c)(f-D=

+

The ter$f / is a !onstant n the stada #or$u(a and s known as the stada or

$u(t"('n. !onstant and $a' be denoted b' the (etter K% The ter$ ( f + c)"art(' o# the

!onstant f and "art(' o# the arab(e c9 wh!h ares as the ob=e!t (ens s $oed n

#o!usn.% oweer the araton n ! s s$a((9 es"e!a((' #or s.hts .reater than 10$9 and

#or a(( "ra!t!a( "ur"oses $a' a(so be !onsdered a !onstant% The ter$ 3 f + c9 usua(('

about B00 to F50$$ n ths te(es!o"e9 s known as the addte !onstant and $a' be

denoted b' the (etter C% Ths redu!es the stada #or$u(a to the s$"(e (near euaton:

CKsD +=

#.(.#.% T)e Analactic &ens

Do you know who J. Porro is?

He is the man who invented the analactic lens

in 1840.

In order to sae the (abour o# $u(t"('n. the sta## nter!e"t ea!h t$e and the

addn. the !onstant #or the "art!u(ar nstru$ent9 t wou(d obous(' be s$"(er # < wereto be 100 and CDero% Ths wou(d "rode a stada #or$u(a o# D6 100s and !a(!u(aton

wou(d $ere(' !onsst o# $on. the de!$a( "ont o# the sta## nter!e"t readn. two

"(a!es to the r.ht% -ost o# the erner nstru$ents st(( n use toda' do not hae an

a!!urate K a(ue o# 1009 but $ost $odern ta!h'$eters .enera((' do% In 1F09 the

e($naton o# the addte !onstant was a!heed b' an Ita(an9 H% orro9 when he

nented the ana(a!t! (ens% The n!(uson o# a se!ond !one* (ens #*ed n re(aton to the

7

si

fcfD =+ 3

3 cfsi

fD ++=


8/48


ob=e!t .(ass had the e##e!t o# brn.n. the a"e* o# the $easurn. tran.(e9 the ana(a!t!

"ont9 nto e*a!t !on!den!e wth the ert!a( a*s o# the nstru$ent9 as ((ustrated n

4.ure 1%5%

4.ure 1%5 The ana(e!t! Te(es!o"e

3Sour!e : and Sure'n.9 Ra$sa' H%% A(son

The ter$f / i6 1/100 be!o$eK6 100% ,stan!e #or # and ! be!o$e s$(ar but n the

o""oste sde% There#ore C 6 0% The stada #or$u(a wou(d now be!o$e KsD = 9 the

addte !onstants are e($nated% Ths e*terna((' #o!usn. te(es!o"e s known as an

ana(a!t! te(es!o"e%

#.(.#.( Evalati-n -f Sta*ia C-nstants

In $ost $odern sure'n. te(es!o"es the stada !onstant s des.ned to be 100 and

the addte !onstant 0% To !on#r$ the a(ue o# these !onstants or to estab(sh the stada

o# an o(d or a new nstru$ent9 the #o((own. #e(dwork shou(d be !arred out 34.ure 1%7

4.ure 1%7 Ea(uaton o# Stada Constants9 < and C

3Sour!e: &sas Ukur


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a Choose a #ar(' (ee( .round

b Set out #our "e.s &9 >9 C9 and , on that .round% &> s 100$9 &C s F0$ and &,

s J0$%! Set u" the ta!h'$eter oer the "e. at & and obsere to a sta## that he(d at C%

d Not the sta## nter!e"ts%

e Trans#er the sta## to , and note the sta## nter!e"ts%

$istance Sta*ia Rea*in/ Staff Intercept

F0

J0

1%7209 1%F2091%220

1%8191%F2190%J81

0%F00

0%J00

Tab(e 1 +bseaton ,ata

3 Sour!e: &sas Ukur


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&s he.ht d##eren!es between sta## "ostons and nstru$ent n!rease9 t w((

be!o$e $"ossb(e to use the horDonta( (ne o# s.ht wh!h so #ar has on(' been

!onsdered% In su!h !ase a ta!h'$eter $ust be used to "rode an n!(ned (ne o# s.ht

and the an.(e o# e(eaton or de"resson $ust be re!orded% The stada #or$u(a $ust nowre#(e!t the an.(e o# n!(naton o# the (ne o# s.ht and two su!h !ases arse:

a where the sta## s he(d ert!a((' at the #ar staton

b where the sta## s he(d to the (ne o# s.ht #ro$ the nstru$ent

#.(.#.0.# Incline Si/)ts 1it) T)e Staff Vertical

4.ure 1%8 shows that an obseraton o# an n!(ned s.ht to a sta## he(d ert!a(('%

&9 L and > are the readn.s on the sta## and &9 L and > are those wh!h wou(d haebeen taken had the sta## been swun. about L to "oston t at r.ht)an.(es or nor$a( to the

(ne o# s.ht%

In #.ure 1%89

s6 the sta## nter!e"t &>

h =the (en.th o# the !entre har readn. #ro$ the sta## base

V 6 the ert!a( !o$"onent LY9 the he.ht o# the !entre har readn. aboe

3or be(ow the nstru$ent a*s

, 6 the (en.th o# the (ne o# s.ht IL

=the horDonta( dstan!e reured%

I 6 nstru$ent he.ht

4.ure 1%8 In!(ne S.ht Ath The Sta## Vert!a(

J


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Example 1:

In this example, the value of hicannot be seen on the rod due to some

obstruction. Here, a rod reading of 2.72 with a vertical angle of -6 7! was

boo"ed, along with the h of #.72 and a rod interval of $.2%#., &alculate the

hori'ontal distance and the vertical distance. (hen find the elevation for station .

)igure #

Solution:

H * #$$scos2+

* #$$ x $.2%# x cos26 7!

* 2.m

* #$$/20 s sin 2+

* #$$ scos Msin M

6 #$$ x $.2%# x cos 6 7!x sin 6 7!

* -2.76m

1..* 1..23 H.I 4 5 h

* #.#6 3 #.72 3- 2.76 5 2.72

* ##.%$

11


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o, the elevation for station is ##.%$,

#.(.#.0.% Incline Si/)ts 1it) T)e Staff -r,al

4.ure 1% shows the obseraton on a sta## he(d nor$a( to an n!(ned (ne o#

s.ht% The sa$e notaton a""(es as n #.ure 1%8%

4.ure 1% In!(ne S.ht Ath The Sta## Nor$a( to The ne o# S.ht

3Sour!e: and Sure'n.9 Ra$sa' H%% A(sonThs t$e the sta## readn. nor$a( to the (ne o# s.ht s the a!tua( readn. and does not

hae to be redu!ed as n the "reous !ase% There#ore

D6KsK C

>ut 6Dkos M 3the dstan!e #ro$ "ont L to the ert!a( throu.h the sta## base

6 3KsK C)!os M hsn M

&s be#ore V 6Dsn M9 there#ore:

V 6 3KsK C)sn M

In nstru$ents where the addte !onstant C s Dero9 < 6 100 and the a(ue o# M s (ess

than 10O 3the assu$"ton s .enera((' $ade that the ter$ h sn M s Dero9 these #or$u(ae

!an be s$"(#ed as :

12


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6 100s !os M

V 6 100ssn M

To obtan the redu!ed (ee( at the sta## staton9 then the he.ht d##eren!e between the"onts s #rst redu!ed as #o((ows:

,##eren!e n he.ht9 d 6 % I% V h !os M

#.(.%.( C-,paris-n -f Met)-*s

C-n*iti-ns Staff -r,al2Staff Vertical

a Ahen

ho(dn. sta##

Sta## !an be he(d ert!a((' wth .reater ease than n the nor$a(

"oston%

Its s$"(er to "(u$b a sta## wth a sta## bubb(e than ho(d the sta##

nor$a( to a (ne o# s.ht%

4or nor$a( ho(dn.9 t needs to be atta!hed wth a "ee")s.ht

"er"end!u(ar to the #a!e o# the sta##9 so the sta##)$an !an s.ht

towards the nstru$ent%

In bush the "ee")s.ht $a' be obs!ured9 "reentn. nor$a( ho(dn.9

wh(e the u""er "art o# the sta## s st(( aa(ab(e #or s.htn. n the

ert!a((' he(d "oston% The nor$a( "oston $a' a(so be #ound b' swn.n. the sta## unt( the

(owest "ossb(e readn. o# the !entre !ross har s obtaned% oweer9

t s d##!u(t to s.na( to the sta##)$an the !orre!t "oston n the bush%

C-n*iti-ns Staff -r,al2Staff Vertical

b Redu!ton

o#

obseraton

The ert!a( sta## redu!ton #or$u(ae are s$"(er than the nor$a(

sta## redu!ton #or$u(a when the hsn M and h!os M are n!(uded

n the nor$a( #or$u(ae%

! Care(ess

sta## ho(dn.

Errors o# dstan!e and e(eaton are er' $u!h $ore $arked when

there s a deaton #ro$ the nor$a( "oston es"e!a((' on stee"

s.hts%

The nor$a( "oston $a' a(so be #ound b' swn.n. the sta## unt( the (owest

"ossb(e readn. o# the !entre !ross har s obtaned% oweer9 t s d##!u(t to s.na( to

the sta##)$an the !orre!t "oston n the bush%

1B


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#.(.% T)e Tan/ential S+ste,

In ths s'ste$ the "ara(a!t! an.(e subtended b' a known (en.th o# sta## s

$easured dre!t('% 4.ure 1%J shows the $ethod where obseratons are taken to anordnar' (ee((n. sta## he(d ert!a(('%

4.ure 1%J The Tan.enta( S'ste$ o# Ta!h'$etr'

3Sour!e: and Sure'n.9 Ra$sa' H%% A(son

The nstru$ent s set u" and the ert!a( !r!(e s read on both #a!es to .e the

an.(e o# e(eaton 3or de"resson to a who(e sta## .raduaton% Ths "ro!ess s re"eated to

another who(e .raduaton to .e as (ar.e a sta## nter!e"t9 s9 as "ossb(e% 4ro$ the sta##nter!e"t and the two obsered ert!a( an.(es M and 9the horDonta( dstan!e $a' be

!a(!u(ated as:

&Y 6 tan M

>Y 6 tan

&Y >Y 6 s

6 3 tan M tan

tan3tan

=s

ortan3tan

=s

3 #or s.ht down h((s

The d##eren!e n he.ht between the nstru$ent staton and the sta## staton s #ound as

#o((ows :

Vert!a( !o$"onent9 V 6 >Y 6 tan

1F


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4.ure 1%10 The rn!"(es o# orDonta( ,stan!e -easure$ent3 Sour!e : Ukur


18/48


4.ure 1%11 The e.ht ,##eren!e >etween Statons

3 Sour!e : Ukur


19/48


Activit+ #a

1%1 Ahat s $eant b' the ter$ ta!h'$etr'P

1%2 E*"(an the bas! "rn!"(es u"on wh!h ta!h'$etr! $easure$ent are basedP

1%B & ert!a( sta## s obsered wth a horDonta( e*terna( #o!usn. te(es!o"e at a

dstan!e o# 112%FJ$% -easure$ents o# the te(es!o"e are re!orded as :

+b=e!te to da"hra.$ 2B0$$

+b=e!te to ert!a( a*s 150$$

I# the readn.s taken to the sta## were 1%08B9 1%72J and 2%159 !a(!u(ate

a the dstan!e a"art o# the stada (nes 3

b the $u(t"('n. !onstant 3K

! the addte !onstant 3C

1%F Ahat are the $an d##eren!es between the stada s'ste$ and tan.enta( s'ste$P

1


20/48


'ee*bac3 #a

' Ta!h'$etr' $eans sw#t $easure$ent where he.ht and dstan!es between

.round $arks are obtaned b' o"t!a( $eans on('%

' The ta!h'$etr' $easure$ents are based on the !o$$on "rn!"(e o# the sos!e(es

tran.(e% The "er"end!u(ar bse!tor o# the base s dre!t(' "ro"ortona( to the

(en.th o# ths base% I# the base (en.th and "ara(a!t! an.(e are known9 then the(en.th o# the "er"end!u(ar bse!tor !an be !a(!u(ated%

1J

Tr' 'our best toanswer these

uestons%


21/48


,stan!e &> 6 ? 3Cd * Cot @/2

I# dstan!e &> 6 ,9 dstan!e Cd 6 S 9so

, 6 ? S Cot @/2

Ahereb'

, 6 dstan!e between two "ont

S 6 base (ne

@ 6 "ara(a!t! an.(e

' 4ro$ euatonD = Ks + C

6 53 cfsi

f++

3 cfD

fsi

+=

150%02B0%03FIJ%112

08B%11I5%232B0

+

=

BI0%0FI%112

100%132B0

=

6 2%B $$

There#ore9 100B%2

2B0===

i

fK

20


22/48

I!"T


C 6 # K! 6 2B0K150

6 B0$$

1%F

In the stada s'ste$9 the a"e* an.(e o# the $easurn. tran.(e s de#ned b' the

stada hars on the te(es!o"e da"hra.$% The base (en.th s obtaned b' obsern.

the nterse!ton o# the stada hars on the $a.e o# the $easurn. sta## seen n the

te(es!o"es #e(d or ew% The tan.enta( s'ste$ n wh!h the a"e* an.(e subtendedb' a bas! o# known (en.th s a!!urate(' $easured9 usua((' wth the sn.(e)se!ond

theodo(te% In order to obtan the dstan!e between nstru$ent and base9 the

tan.ent o# the an.(e or an.(es obsered $ust be used n the !a(!u(aton%

Well done. You have done a good job!!

#.0 STA$IA 'IE&$ !RACTICE

Stada ta!h'$etr' s $an(' used n sure'n. deta(s n se(e!ted areas% &deuate

horDonta( and ert!a( !ontro(9 su""(ed b' traersn. and (ee(n. s reured to orentate

the sure' and to "rode staton (ee(s% It s best suted to o"en .round where #ew hard

(ee(s are reured%

21


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" 4na((' redu!e the notes 3!o$"ute horDonta( dstan!es and e(eaton a#ter

#e(d hours and !he!k the redu!tons%

4.ure 1%12 Stada 4e(d Aorks%

3Sour!e: Ukur aharn -oha$$ad

2B


25/48

C 2005 / 2 /

ENGINEERING SURVEY 2

#.0.% Rec-r*in/ -f Observati-n

Stada ta!h'$etr' s best booked n tabu(ated #or$ as be(ow%

Stati-n an*

Instr,ent

Hei/)t

H-ri5-ntal

An/le 678

Vertical

an/le

Mi**le

Sta*ia

rea*in/

Sta*ia

rea*in/

6a 9pper

rea*in/8

b: l-;er

rea*in/8

H-ri5-ntal

&en/t)

H < 4s

C-s%=:C

Vertical

*ifference

VH < Hi

?V:)

Re*ce*

level -f

stati-n

Re*ce*

level -f

p-int

Re,ar3s

Staton 2

1%5F2$

50 2B 00 K B1 0%7$ a) 0%J0

b) 0%B10

58%J71$ 1%501$ 2%FFB$ 100 102%FFB$ Staton 1)

!ontro( staton

BFB 25 00 )J2 B2 0%5$ a) 0%551

b) 0%FFJ

10%07$ )1%15B$ )0%111$ JJ%J$ a) besde

drana.e

BF2 58 00 ) J7 B7 0%F$ a)0%F5F

b)0%BF7

10%758$ )1%2BB$ )0%0J1$ JJ%J0J$ b) besde

drana.e

B58 00 00 )J7 20 0%$ a)0%B8

b) 0%87B

8%BF0$ )0%11$ )0%07J$ JJ%JB1$ !) road sde

B05 B1 00 )JF 2 1%2$ a)1%2F2

b)1%5F

%B5B$ )0%752$ )0%B10$ JJ%7J0$ d)tree 3radus)

2%8$

21F 17 00 )JF B8 1%2$ a) 1%2B0

b) 1%180

5%J71$ )0%F1$ )0%1BJ$ JJ%71$ e) besde

drana.e

220 B8 00 )JF 05 1%B$ a) 1%B27

b) 1%28F

5%18F$ )0%B7J$ )0%128$ JJ%8B$ #) besde

drana.e

250 B7 00 )JF 07 1%B$ a) 1%BBF

b) 1%277

7%875$ )0%F5$ )0%2FB$ JJ%858$ .) (a$" "ost

255 27 00 )JF 2B 1%B a) 1%B2B

b) 1%288

F%58B$ ))0%B51$ )0%10J$ JJ%J1$ h) road sde

Tab(e1%1 Ta!h'$etr' Stada -ethod >ookn.


2F


26/48


27/48


wth the (en.th o# s.ht% The obous so(uton s to ($t the (en.th o# s.ht

to ensure a .ood reso(uton o# the .raduatons%

Error n the deter$naton o# the nstru$ent !onstants


28/48


4.ure 1%1B Errors In E(eaton%

3Sour!e : En.neern. Sure'n.9 A% S!ho#e(d

#. !&OTTIG

ter the #e(d obseratons9 the !o((e!ted data $ust now be "ro!essed% The

traerse !(osure s !a(!u(ated and then a(( ad=usted a(ues #or northn.9 eastn. and

e(eatons are !o$"uted $anua((' or b' !o$"uter "ro.ra$s% ter that9 the data s

"ro!essed b' usn. so#tware su!h as TRS and &uto!ad% &(( the deta(s !an be "(otted the

#o((own. wa'%

a (ottn. Contro( Staton%34.ure 1%1F

(a!e the !ontro( staton on a .rd "a"er%

The .rd "a"er s "rnted wth .rd (nes at 1$$ ntera(s%

Ahen "(ottn. on .rd "a"er9 the statons are de#ned b' usn. the

!oordnate s'ste$%

Staton 1 s assu$ed as the or.n whereb' !oordnate * s 1000$ and

!oordnate ' 1000$% The "oston o# staton s "(otted startn. #ro$ the(ower (e#t !orner o# the .rd "a"er%

S!a(n. a(on. the *)a*s #ro$ !oordnate * staton 19 "(ot the !oordnate o#

staton 29 L2% Usn. the sa$e wa' a(so "(ot !oordnate Y2% Re"eat ths

ste" #or staton B and staton F

28


29/48


4.ure 1%1F ,eter$naton +# Staton oston +n Grd a"er%


b ,eta(n. 34.ure 1%15

Instead o# usn. !oordnates9 "(ottn. !an be done b' s!a(n. the bearn. and

dstan!es o# a deta(%

Nor$a((' a "rotra!tor and a s!a(e ru(er are needed n "(ottn.%

(a!e the !r!u(ar "rotra!tor wth ts !entre staton 2 and the Dero (ned u"

wth the re#eren!e staton 2)1%

-ark the bearn. o# a on the "a"er a.anst the "rotra!tor ed.e%

Re$oe the "rotra!tor and draw the dre!ton o# the (ne 2)a% S!a(e the

dstan!e and "(ot the "oston o# a%

Re"eat the sa$e ste"s when $arkn. o## "ont !)=%

4na(('9 =on the "onts to #or$ the deta(%

2


30/48


4.ure 1%15 ,eta(s (ottn. +n Grd a"er%3Sour!e: Ukur aharn -oha$$ad

! Contours

ter $arkn. a(( the deta(s9 the !ontours need to be "(otted%

Contours are (nes on a $a" re"resentn. a (ne =onn. "onts o# eua(

he.ht on the .round% Ths $ethod s $ost !o$$on(' ado"ted #or (ar.er

areas%

Redu!ed (ee( s "(a!ed besde deta(s and the he.ht o# ea!h "ont s

s"otted%

4na(('9 !ontour (nes are "(otted b' usn. the nter"o(aton $ethod%

d re"araton o# Tt(e >(o!k on Tra!n. a"er%

&(( to"o.ra"h' and en.neern. drawn.s hae tt(e b(o!ks%

Usua((' the tt(e b(o!k s "(a!ed n the r.ht !orner o# the "(an9 wh!h a(so

has the (o.o !(ent9 "ro=e!t na$e9 date o# "ro=e!t and other deta(s%34.ure

1%17%

2J


31/48


Resons to the "(an are usua((' re#eren!ed $$edate(' aboe the tt(e

b(o!k9 shown. the date and a bre# des!r"ton o# the reson%

The tt(e b(o!k s o#ten o# standard sDe and has a #or$at s$(ar to that n

#.ure 2%F%

&(( the drawn.s on tra!n. "a"er are done $anua((' b' usn. the

te!hn!a( "ens wth Indan nk or b' usn. &utoCad so#tware%

The sDe o# the te!hn!a( "en s deter$ned based on te*ts and (nes

reured n a drawn.%

4.ure 1%17 Tt(e >(o!k


e 4na( drawn.%

ter !o$"(etn. the tt(e b(o!k9 trans#er a(( the drawn.s #ro$ the .rd

"a"er to tra!n. "a"er%

Then9 wrte the addtona( te*t or draw (nes and s'$bo(s n that drawn.%

The te*ts re#er to the na$e o# bu(dn.9 road9 and a(ues o# he.ht and

!ontour ntera(s%

(ot the te*t horDonta((' #or a(( a(ues e*!e"t the a(ue o# he.ht%

Eer' deta( has (nes o# d##erent t'"es and sDes% 34or e*a$"(e9 the root

(ne o# hed.e s shown n b(a!k and the out(ne n .reen

4na(('9 "(ot the deta(s b' usn. a "(otter% 34.ure 1%18%

B0

S!a(e

,re!ton

Grd a(ueo o !(ent

(an nu$ber

(an tt(e

,atu$ e* (anaton

e end

E*"(anaton o# obseraton9 and Sure'

4r$9 Na$e o# sure'or9 date9 "(an re#eren!enu$ber and others%


32/48


4.ure 1%18 ,eta(s That (ot +n & )en (otter%

3Sour!e: Sure'n. Ath Constru!ton &""(!aton9 >%4%


33/48


At stati-n &

Gri* ref E F009 NB00

1eat)er C(oud'9!oo(

Stn level 6R&8 B0%F$ +,

Ht -f inst 6)i8 1%F2$

ADis level 6R& )i8 B1%J0$3&*

Srve+ Canbur' ark

Srve+-r H% S-IT

$ate 12%12%B

Staffp-int

An/les -bserve* Staff rea*in/s

Staffintercept

H-ri5-ntal$istance

4s c-s%=

VerticalAn/le

42% s sin

% =

Re*ce*level

Re,ar3H-ri:

5-ntal

Vertical

circle

Vertical

an/le

s , V &* V)hR+ 0 00 Staton >

1 FO12 J5O20 )5O20

1%JF2

1%F0F

0%77

1%087 107%78 )J%J7 20%5F Ed.e o#

"ond

2 0O02 JBOF0 )BOF0

0%JJ

0%7F0

0%21

0%818 81%F1 )F%5 27%7 Ed.e o#

"ond

B 108O57 BO20 K7OF0

1%710

1%217

0%22

0%8 88%8F KJ%0J BJ%88 Ed.e o#

"ond

Tab(e 1%2 >ookn. +# 4e(d ,ata


4.ure 1%1 ,eta( Sure'


B2


34/48


#..% C-nt-rin/

Contourn. s !arred out e*a!t(' the sa$e $anner as aboe9 but wth $an' $ore

s"ot shots a(on. ea!h rada( ar$ 34.ure 1%1J% The ar$s are turned o## at re.u(ar an.u(ar

ntera(s9 wth the sta## $an obtann. (ee(s at re.u(ar "a!ed ntera(s a(on. ea!h ar$

and at ea!h dstn!t !han.e n .radent% Subseuent !o$"utaton o# the #e(d data w(( #*

the "oston and (ee( o# ea!h "ont a(on. ea!h ar$9 wh!h $a' then be nter"o(ated #or

!ontours%

4.ure 1%1J Contourn.


#.F '"RTHER O!TICA& $ISTACE:MEAS"RIG E"I!MET

#.F.# $irect:Rea*in/ Tac)+,eters

,re!t)readn. ta!h'$eters or se(# redu!n. ta!h'$eters as the' are a(so !a((ed9

hae !ured (nes re"(a!n. the !onentona( stada (nes% 4.ure 1%20 ((ustrates one

"art!u(ar $ake9 n wh!h the outer (nes are !ures to the #un!ton !os2and the nner

!ures are to the #un!ton sn!os% Thus the outer !ure sta## nter!e"t s not =ust S but S

!os2% en!e9 one need on(' $u(t"(' and nter!e"t readn. b'


35/48


There are other $akes o# nstru$ents wh!h hae d##erent $ethods o# dern. at

the so(uton% oweer9 the ob=e!te re$ans the sa$e)to e($nate !o$"utaton% It

shou(d be noted that there s no $"roe$ent n a!!ura!'%

4.ure 1%1J +uter nes o# ,re!t)readn. ta!h'$eters

3Sour!e: En.neern. Sure'n.9 A% S!ho#e(d

#.F.% Vertical:Staff !recisi-n Tac)+,eter.

The ert!a()sta## ta!h'$eter as "rodu!ed b'


36/48


4.ure 1%20 orton o# Vert!a()Sta## re!son Ta!h'$eter%

3Sour!e: En.neern. Sure'n.9 A% S!ho#e(d

#.F.( T-tal Stati-n

Ahen e(e!tron! theodo(tes are !o$bned wth nter#a!ed E,-Is and an

e(e!tron! data !o((e!tor9 the' be!o$e e(e!tron! ta!h'$eter nstru$ents) Tota( Statons%

The tota( statons !an read and re!ord horDonta( and ert!a( an.(es to.ether wth the

s(o"e dstan!es% The $!ro"ro!essors n the tota( statons !an "er#or$ a aret' o#

$athe$at!a( o"eratons9 #or e*a$"(e9 aera.n. $u(t"(e an.(e $easure$ent9 aera.n.

$u(t"(e dstan!es $easure$ent9 deter$nn. L9 Y9 Q !oordnates and others% The data!o((e!ted !an be hand(ed b' a de!e !onne!ted b' !ab(e to the ta!h'$eter but $an'

nstru$ents !o$e wth the data !o((e!tor bu(t nto the nstru$ent%

,ata are stored on board nterna( $e$or' about 31B00)"onts and on $e$or'

!ards 3about 2000 "onts "er !ard% The data !an be dre!t(' trans#erred to the !o$"uter

#ro$ the tota( staton a !ab(e9 or the data trans#erred #ro$ the data stora.e !ards #rst to

a !ard reader)wrter and #ro$ there to the !o$"uter% Ths se!ton w(( be ds!ussed #urther

n Unt 7%

B5


37/48


4.ure 1%21 Tota( Staton

3Sour!e: Sure'n. Ath Constru!ton &""(!aton9 >%4%


38/48


Activit+ #b

1%5 st down 5 ste"s that are needed to "rodu!e a to"o.ra"h! $a"%

1%7 The #o((own. obseratons were taken wth a ta!h'$eter9 han. !onstants o#

100 and Dero9 #ro$ "ont & to > and C% The dstan!e >C was $easured as 158$%

&ssu$n. the .round to be a "(ane wthn the tran.(e &>C9 !a(!u(ate the horDonta(

dstan!e and ert!a( dstan!e #or &>%

At T- Staff rea*in/s 6,8 Vertical An/le& > 1%F9 2%8B9 B%J K 8B7C 2%09 2%29 B%57 )52F

1%8 In ta!h'$etr' sure'9 the a!!ura!' o# stada obseraton s a##e!ted b' seera(

sour!es o# error% ,es!rbe B o# these errors%

1% ,es!rbe the "ro!edure to $"(e$ent the stada #e(d work n ta!h'$etr' sure'%

B8

Look for the

solutions

now.


39/48


'ee*bac3 #b

1%5 There are 5 ste"s to "rodu!e a to"o.ra"h! $a"%a (ottn. Contro( Staton

b ,eta(s "(ottn.

! Contoursd re"araton o# tt(e b(o!k on tra!n. "a"er%

e 4na( drawn.

1%7 orDonta( dstan!e &> 6 100 * S !os2

6 100 * 3B%J 1%F !os2 8B7 6 2F7 $

Vert!a( dstan!e &> 6 2F7 tan 8B7

6 KB2%$

1%8 There are three knd o# errors:

a Care(ess sta## ho(dn.% Ths s $n$Ded b' usn. sta## bubb(es%

b Error n readn. the stada nter!e"ts% Ths sour!e o# error w(( n!rease wth

the (en.th o# s.ht% The obous so(uton s to ($t the (en.th o# s.ht to

ensure .ood reso(uton o# the .raduatons%

! E##e!t o# d##erenta( re#ra!ton on the stada nter!e"ts% Ths s $n$Ded b'kee"n. the (ower readn. 1 to 1%5$ aboe the .round%

1% Estab(sh F !ontro( statons 3staton 19 staton 29 staton B and staton F b' usn.wooden "e.s%

I$"(e$ent horDonta( !ontro( networks on ea!h% Re!ord the data n a #e(d book%

ter that9 $"(e$ent the (ee((n. "ro!ess to .et the e(eaton o# ea!h staton%

Re!ord the obseratons n the #e(d book%

Now9 use ether stada ta!h'$etr' $ethod or stada e(e!tron! $ethod to set the

theodo(te oer staton 2%

-easure the he.ht o# the theodo(te at staton 2 as 2wth a stee( ta"e%

Set the horDonta( !r!(e to Dero%

S.ht the re#eren!e staton 3Staton 1 at 0O00%

S.ht the stada "ont to Staton B b' (oosenn. the !(a$" 3!(a$" s t.ht%

S.ht the $an horDonta( har rou.h(' on the a(ue o# h9 then $oe the (ower har

to the !(osest een #oot 3de!$eter $ark%

Read the u""er har9 deter$ne the rod ntera(9 and enter the a(ue n the notes%

S.ht the $an horDonta( har "re!se(' on the h a(ue%

B


40/48


41/48


Self Assessment

1 Ta!h'$etr' s used to deter$ne the e(eaton o# the nstru$ent staton > base on

e(eaton o# staton &% E*"(an the ta!h'$etr' stada #or$u(a be(ow b' usn.

((ustratons%

R%%>6 R%%&K %I K V h

Ahere:

R%%> 6 e(eaton o# the nstru$ent staton >

R%%&6 e(eaton o# the nstru$ent staton &

%I%6 nstru$ent he.ht

h =the (en.th o# the !entre har readn. #ro$ the sts## base

V 6 the ert!a( !o$"onent LY9 the he.ht o# the !entre har readn. aboethe nstru$ent a*s

2 & (ne o# thrd order (ee((n. s run b' theodo(te9 usn. ta!h'$etr' $ethods

wth a sta## he(d ert!a(('% The usua( three sta## readn.s o# !entre and both stada

hars are re!orded to.ether wth the ert!a( an.(e 3V&% & se!ond a(ue o# he.ht

d##eren!e s #ound b' a(tern. the te(es!o"e e(eaton and re!ordn. the new

readn.s b' the ert!a( !r!(e and !entre har on('%

The two a(ues o# the he.ht d##eren!es are then $eaned% Co$"ute the d##eren!e

n he.ht between the "onts & and > #ro$ the #o((own. data:

The stada !onstant are :$u(t"('n. !onstant 6100; addte !onstant 6 0%

Bac3si/)ts

VA

Staff '-resi/)ts

VA

Staff Re,ar3s 6all

,easre,ents in ,8

K 0O 02 00W 1%J0

1%F18 ont &

0%JF5

K0O 02 00W 1%J0

)0O 1 00W B%10J ont >

2%0120%J1F

0O 00 00W B%171

3he.ht d##eren!e between the two ends o# theodo(te ra' 6 100s !os M sn M9 where s6

stada nter!e"t and M 6 V&

B The rod readn. $ade to !on!de wth the a(ue o# the hi9 s t'"!a( o# J0 "er!ent

o# a(( stada $easure$ents% In #.ure 19 the ert!a( an.(e s K 1O B7 and the rod

F0


42/48


ntera( s 0%F01% >oth the rod hiand the rod readn. 3R%R% are 1%82$% Ca(!u(ate

the horDonta( dstan!e and the ert!a( dstan!e% Then #nd the e(eaton #or

staton 2%

%

'i/re %

F & theodo(te has a ta!h'$etr' !onstant o# 100 and an addte !onstant o# Dero%

The !entre o# readn. on a ert!a( sta## he(d on a "ont > was 2%2J2$ when

F1


43/48

'ee*bac3 t- Self Assess,ent


s.hted #ro$ &% I# the ert!a( an.(e was K25and the horDonta( dstan!e &> s

1J0%B27$9 !a(!u(ate the other sta## readn.s and thus show that the two nter!e"t

ntera(s are not eua(% Usn. these a(ues !a(!u(ate the (ee( o# > # & was

B8%J5$ and the he.ht o# the nstru$ent 1%B5$%

5 The tab(e be(ow shows a ta!h'$etr' stada #e(d bookn.% Co$"(ete the tab(e

be(ow and !a(!u(ate e(eaton o# ea!h "ont%

Stati-n

an*

instr:

,ent

)ei/)t

H-ri:

5-ntal

An/le

678

Vertical

an/le

Mi**le

Sta*ia

rea*in/

a 9pper

rea*in/

b: l-;er

rea*in/

H-ri5-nt

al &en/t)

H < #s

C-s%=:C

Vertical

*ifference

Vesde

road

1801)J

F1%120

1%252

1%000a$" "ost

12021 8 F7 2%2022%F85

2%100

Centre

(ne

F2

How to

answer

this???

Try your best

to find thesolution.


44/48


1

The #.ure aboe shows

R%%>6 R%%&K %I K V h

Ahere:

R%%> 6 e(eaton o# the nstru$ent staton >

R%%&6 e(eaton o# the nstru$ent staton &%

%I%6 nstru$ent he.ht

h =the (en.th o# the !entre har readn. #ro$ the sta## baseV 6 the ert!a( !o$"onent LY9 the he.ht o# the !entre har readn. aboe

the nstru$ent a*s

2 V 6 100s sn M !os M

6 50s sn 2 M

To &9 V 6 50 31%J0 )0%JF5 sn 0O 0F 00W

6 0%055$

,##eren!e n (ee( #ro$ nstru$ent a*s 6 0%550 1%F18

6 )1%B72

Check .ea&in

V 6 50 30%JF5 sn 0O F0 00W

FB

Theodo(te

Sta##


45/48


6 0%550$

,##eren!e n (ee( #ro$ nstru$ent a*s 6 0%550 )1%J0

6 )1%B5

-ean 6 1%B70$

To >9 V 6 50 3B%10J)0%J1F sn )0O B7 00W

6 )1%1FJ$

,##eren!e n (ee( #ro$ nstru$ent a*s 6 )1%1FJ)2%012

6 )B%171

Che!k (ee( 6 )B%171

-ean 6 ) B%171$

,##eren!e n (ee( &> 6 )B%171K1%B70

6 )1%01$

B 6 100s!os2M

6 100 * 0%F01 * !os21O B7

6 F0%1$

V 6 3100/2s sn 2M

6 100s!os Msn M

6 100 * 0%F01 * !os 1O B7* sn 1O B7

6 K1%12$

R%%26 R%%1K %I V h

6 15%17 K 1%82 K1%12 1%82

6 17%2

So9 the e(eaton #or staton 2 s 17%2%

F

FF


46/48


4.ure 1

4ro$ bas! euaton9 C, 6 100s !os2M

1J0%B27$ 6 100 s !os225

s 6 2%B17$

4ro$ #.ure 19 H 6 s !os225 6 2%B17 X !os225 6 2%1$

In!(ned dstan!e CE 6 C, se! !os225

U2BRBF0210

1%22 == ra&

U11R180=

Now b' re#eren!e to #.ure 1:,G 6 C, tan 325- 6 1J0%B27 tan 325)0 18 11W 68%5JF

,E 6 C, tan 25 6 1J0%B27 tan 25 6 %8FJ

,4 6 C, tan 325K

6 1J0%B27 325 K 0 18 11W 6 J%J10

It !an be seen that the stada ntera(s are:

GE 6 ,E ,G

F5


47/48


6 S1 6 %8FJ 8%J5F

6 1%115

E4 6 ,4 ,E

6 S2 6 J%J10 %8FJ

6 1%171

4ro$ wh!h t s obous that the a U""er readn. 6 32%2J2 K1%171 6 B%F5B

b ower raedn. 6 32%2J2 1%155 6 1%1B8

Vert!a( e.ht ,E 6 h

6 C, tan 256 1J0%B27 tan 25

6 %8FJ3 as aboe

ee( o# > 6 B8%J5 K 1%B5 K %8FJ 2%2J2

6 125%858 $

5

F7

62%B17

3Che!k

CD = s "os#$%..&'la

bla bla(


48/48


Stati-n

an*

instr:

,ent

)ei/)t

H-ri:

5-ntal

An/le

678

Vertical

an/le

Mi**le

Sta*ia

rea*in/

a 9pper

rea*in/

b: l-;er

rea*in/

H-ri5-nt

al &en/t)

H < #s

C-s%=:C

Vertical

*ifference

Vesde

road

1801)J

F1%120

1%252

1%0002F%710 B%10 7%J0F

b )a$"

"ost

12021 8 F7 2%2022%F85

2%100B8%FFB 1%F70 11%0J2 !)Center (ne

Redu!ed (ee( o# "ont a 6 10%F18 K1%F18 )0%210 B%100

6 %52F

Redu!ed (ee( o# "ont b 6 10%F18 K1%F18 )B%10 1%120

6 7%J0F

Redu!ed (ee( o# "ont ! 6 10%F18 K1%F18 K 1%F70 2%202

6 11%0J2

F8

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