-
PN = l7.OO kg:f il7.oo) = il7.oo)5 - 5il7.OO)2 - 4044.96-= -
576.96
;
PN = 17 .5O kg:fil7.50) = il7.60)5 - 5il7.50)2 - 4044.96 =
-2t6.83PN = 17,78 kg:t(n.7e') = u7.78f - S l7.7ef - 4044.96 = -
4.AC
Try
'f ry
Try
Try PN = t7.79kg:f UT.7gl " ur.79t3 - 5u7.7g)z - 4044.96 = +
z.g7
Try Pn = 17 .8O kg:t itz.eot = il7.Bof -s (ft.ao'tz - 4044.96 =
+ to.59
From tha obove five triols, it con bs seen thot the volue of px
whichgives o solution neoresl to zero is 17.79 kg, therelor",-Fp:
f,ZlZS kg. fhexoct volu is ac?uolly somewhere between- lz.zg- ond'
ti'.zg kg. Sifice'-only two digits ofter rhedecimor potnt- woull
tii'iutt'iiieni', the votua tz.zgwos selecled.
IOR ue.iunEt.tr ILesson ll
-.Wgiif,ff.g. -[o!,
I}TEASUNEIfiENTOF IIONTZONTALDISTANCES
l
n-,. curBTlE c0RREcTrolrstt-t. suRvEys ulTH TME
l. Etprting Pe4etdiulan To Litoal Chnd-Bi.uttion kthodbl 3:1:5
llelhod
2. thr.attLing Atgl2A Uith Tape.3. tqitg o{l AtrgbL Uifi Tape1.
Oetehinhg Obeunted Oi.ttarcet
tr-t. il.r.us'n nvE PR6rEl{st. Cffiinen Cor,r:ettioru2. Cortinen
Conxettiorut. Cffiinen Cotuegtiona1. ,btutring Anglz,s Uith Tape5.
,eaatilLitg Angfra Uitth Tape.6. Atuhuctun gi,ttarcet
-
11-1. COXBTf,ED CORABCTTOIfS.The correctionE for the ef,fects of
lncorrect length of,tape, ternperature, tension, alope, and sag
rnay be comblnedas a single net correctisn per tape length. Each
correctlonis computed separately and lt ls lnportant to
ldenttfywhlch correction tends to nake the taPe too I'onq or
tooshort.
Since the sign of each correction can be determined du-rlng
computation, it is then a matter of addlng these guan-tities
algebralcally to arrlve at a single and overall cor-rection to
lengths vhich are measured or lald out. Comblnedcoirections are
usually determlned on the basls of thcnominal tape length siice
each correctlon is relatlvelysmall and do not appreciably affect
each other. The result-ing net correction per tape length nay bq
used as long atconditions renain constant during taplng. Variation
in con-ditlons mry be due to changes ln temperature durinQ thalday,
non-uniformity of pull exerted on the ends of thataF, the ground
may be such that it becones necessary toEupport the tape at varlous
lntervala, and some othcrfactors which may affect the taping
operatlon
11-2. ST'RYBTS gITH TIPE.The tape is'not necesEarily linlted
only to the measuremsntof distanceE. There are various problems
arlsing in survey-lng fiel.duork whlch can be solved just by the
use of Itape. Some of thgse surveylng operatS.ons include:
erecttngpbrpendicular to a line, measuring angles, laying off
ang-Ies, determining obstructed diEtances, locating
irregulr!bounderies, and determlning, areas of dlfferent shapes.
:
1. Erectlng Perpendicular To Line. There nay be 6instances when
it would be necessary to erect on the groa perpendicular to an
eEtablished line. For example,the floor dlmensions of a building or
aare to be laid out, it becomes necessarycular lines. Commonly
employed for suchments are the chord-bisectlon method and
road interseetlto erect perpendlparticular regulrlthe 3ltl:5
method.
a) Chord-Blsectlon lGthod. In Flg. l1-1' lt ls ragulred to
erect.a perpendlcul.ar to the }Ine AB at polnt ITwo egual lengths,
tlb and rc, are measured on each side opoint n. htith b as center
and taking any convenient Lof tape as radlusr iln arc of a clrcle
la descrlbed.same procedure is repeated at point c. The
intersectlon othe two arcs locate'polnt d, and line dn ls the
deglperpendicular to AB.
b) 3:l:5 llethod. This method of erectlng a perpendlcular to a
given llne is illustrated ln 8ig. 11-2. Thcthod involves the
setting up on the ground of a tltanguhose three sldei are made ln
the proportlong of 3,,l lO- ltftff#tlicfhs
,lFIe. ll-1. Cticrd-bdrnrjol- nntd. Fig. ll-r. l-1-i nfrd.
5. Polnt A ls seleqted on line X}f, where a perpendicular isto
be erected. From A and along llne MN, measure 3.0 m totet polnt 8.
Then, with the zero end of the tape held bythe flrst tapeman at B
and the 10-n mark held by the secondtepernan at A, a loop ls formed
by the third tapeman tobrlng the 5-m and 6-m marks together. The
third tapenanthan pulls each part of the tape taut tcj locate point
C onthc Around. The ltne joining polnts A and C ia the
desiredgrrpendlcular to llne HN.Althouqh thls task is better and
e4sier performed bythree tapemeno it is st1l1 posaibl.e for Just
one person togrrform the layout by fastening the tape ends to
stakeslrcurely anchored at polnts A and B. Alsoi any otheftrngths
ln the proportlons of 31 4, and 5 can be used Euchtr 5:8:10,
9:12:15, and L2zL6z2O.
2. l{easurlng Anglea lltlr Ta5n. A tape ls not frequent-ly used
ln engineering condtructions for measqring or lay-llt. ,l-t.
,at^saing atryrl bg ahrlrd rhd.
Itlhere:l- e ony convenicnt length(; chord dlsloncaQ. = ongle to
be meosured
,,c,frrrWitfhti
-Jll
tItttIIII
tf2
--\It,
IIttI
tf2
I
-
lng out angles. There may be some occaslons, however, whena
theodorite or transit is not readlly avallabre that thetape is
instead used. The measurement of very smalr angleswlth tape
usual].y gives satisfactory results. Arl angurarmeasurements by
tape are accomplished by the apprication of
the aielevery basic geometric and trigonometric principles.In
Fig. 11-3, let it be reguired to measureBOC (orO). One way to do
it'is to lay out anylength (L) along lines oB and OC to
establish-b, If the chord distance ab (or d) is'measureded, the
angle BOC can be c.omputed as folLoys
convq.qient'points-i andand blsect-
/
' sintlt'Y Eq'(l)Equation 1 is only valid if the lengths of Oa
and, Ob areequal. If unegual lengths are laid out, as AB and AC
inFig. 11-4, then upon measuring the distance gC, the anglcBAC
(or{A) can be computed using any of the following tri-gonometric
equationsFiA. ll-1. ,kt.str.ilg atqlt uith tape..
A -
(AC)z+(AB)2-(BC)e@
lfhete AB, AC, and EC are the sides of triangle ABC and S(L/21
(AB+AC+BC).The accuracy of measuring angles with tape depends,the
care taken in laylng out lengths and in establ,isfrlthe needed
points on the ground. It would be dlfficult
measure angl.es when the terrain is very irregular or
rhetavegetation obstructs the desired measurement.
The use of the tape in measurtng angles ls rather sland should
only be empJ.oyed on aurveys covering relatlvelsmalI areas. A
transit or theodolite should be used to meesure or lay out angles
on surveys of wlder scope and wtrerdhigher degrees of precision
would be required.3. Laying Off Angles Uith Tape. There are
diffezent mr-thods which may be used to lay off an angle using a
tapa.In F'ig. 11-5 ls illustrated a method vhlch employa a
alprinciple of trigonometry. Along line AB a convenlcntlength, AP,
is first laid out. Then pp' is erected perpcn-dlcular to the llne
at P by using a length whlch ls detcr-mined by multiplying the
1engtn oi ap toi'f,) by the naturrltangent of ,the angle to be lald
off or ppt = ! (Tan0l.Aqgle PAP| (or0) should glve the desired
angle at A.'Another method reguires the determlnation of a chorCl,
t taatutEvatr uI r 1G- H*tqt4 Urtreaa
fig. tl-5. Lulutg ol[ at an4ltwhg a pe4enniuilat li*.
tag. ,r-6. taqing oll an atglttuitts. o ehud langth.
\
Ec.(31
Icngth whtch will define the desired angJ.e. In Fig. 11-6,tt is
required to Lay off an angle fn (or0) from line PA.The chord length
is first determined from the iiquation d =ZLaLnlQ/2), where g is
the desired angle and L is any con-venient length laid out along
tine PA. Then, point n isrstablished by laying out from P, and
along line PA, aconvenient length of tape. The tape is then swung
throughln arc and accordingly the arc traced is marked on
theground. Wlth ! now as center, the computed chord length is1160
laid out and swtrng through an arc, and its inter-rection wlth the
first arc establishes point n. Line nn isthe required chord length,
and the angle fn is the desiredrngle.
oeterrrning obstructed Distances. rn some instancestt may not be
possible to directly measure distances due toen obstruction. The
required J.ength lnay also be inaccessi-ble or difficult to
measure. The fol.lowing are some of thelndirect methods which could
be employed to determine obs-tructed or lnaccessible distances
a) In Fig. 11-7, point C is established at a conve-nlent
location away from the obstruction and it is seen toIt that lines
AC and BC intersect at right angIes. BothIlnes are measured as
accurately as possible. If A and Bdefine the end points of the
required llne, the length ofltne AB can be computed by the
pythagorean theorem or
ABg Eq.(4)b) The length of llne AB ln F19. 11-8 could not be
determined because of an obstruction somewhere at the mid-dle of
the llne. To dbtermine its length, the head tapemananchors one end
of the tape at B and swings it using anyconvenient radius. The rear
tapernan positions himself atpolnt A and llnes in the other end of
the tape with a dis-tant polnt as D and directs'ttre marking of
points a and bon the ground where the end of the tape crosses line
AD.Tha mld-pbint of llne ab is located to establish point C.
*,f&?!["o15ll{,
-
l13.
-
llal| /.,
-u,3Ob!l ruclion
Fig. rr-7. Fig. tl-t.
Flg. ,l-9.
Fis. ,r-r0
I l4- itiifrjff{,ofio,"*&';fi1!"iili:*%
-
I 15,
\lftn 1ln9 BC eatabllahcd pctptndlcular to llnc AC, thclcngth oE
AB can be tndlrsctly,detcrmlned also by thcpythagorean theorem
slnce AC and BC are known.
c, In Flg. 11-9, the length of AB.can be determineddue to the
slnilarlty of triangl.es ABD and BCD. A line' BDof predetermlned
length is first established $erpendicularto llne ABC. The length of
line BC is then measured and ABls computed as fol lows:
# = 3 or AB " (BD)2^Bc). . . . . . . . Eq.(5)d) The length of AB
in Fig. 11-10 is determined by
using the tangent function of trigonometry. At a
convenientlocatlon along the shore Ilne, AC is set out
perpendicular'to AB and lts length measured. tlith the use of a
tape,angle BCA is determined by the chord method. The
reguiredlength is then determined as follows
AB = (AC) Ton ({BCA} " " 'Eq.(6)e) In Fig. 11:11, polnt C'ls
established at a sulta-
ble location away from tbe.obstruction and the lengths ofAC and
BC are measured. On the extension of both linesr'potnts D and E are
established such that CD = (Ac)/2 and CE= (BCl/2. The length of AB
is parallel to and twice' theIength of DE which can be
measured.
fl The method illustrated in Fiig. 11-12 is one wheretwo 1lnes,
BD and CE, are established perpendlcqlar to theline ABC. The
distance betueen the two perpendiculars (orBC) is measured an with
polnts D and E both lined up withA, the length of AB can then be
determined by similarity oftriangles or
g =
(AB j- Bc) i AB (cE) = BD {AB + Bc)BD CEAB (CE) = BD (AB) +
BD(BC)AB (CE) . BD (AB) = BD ( BC)AB (cE. BD) - BD(BC) or AB = ffi.
. Eq.(7)
g) In Flg. 11-13, it is required to deternine thelength of line
AB which apparently could not be measureddlrectly because of an
intervening body of water. The re-quired length ls determined by
establishlng a Iine cD whichis parallel to and equal ln tength to
A8. In thiq method,.perpendicular offsets AC and BD are established
by tape. IfAC and BD are egual in length, CD, when measured, should
beequal to the length of AB
- h) In Fig. 11-14, the obstructed length of AB may belndlrectly
determined if the length DE can be measured. Inthls rnethod, polnt
C is first selected such that it is a
-
llA teatunatEtr 6
errtaln dtctancG away from the obatructed llne. The lengthsof AC
and EC are then meaaured and thelr respective middlepotnta (D 6 E)
establlshed.. The length of AB is ttrice thatot DE
1) One convenient method of getting around obstruct-tonc such as
a large building, involves uslng an equilate-rel trlangle as
illustrated in Fig. 11-15. From the prolon-getlon of the preceding
llne, a 60-deg angle is laid off atA and a sufficient length is
laid out to cleai the obs-tructlon. Another 50-deg angle is laid
off at C and thedlatance CB is taped equal to AC. Point B should
fall 'onthc prolongation of the original line and the
measurement'rney be continued further. The length of AB should be
equalto elther AC or CB..
J) Shown in Fig. 11-16 is a typical problem encoun-tcred when
determining the width of a stream or a tride ri-vcr. Here, BD is
set out perpendicular to the requiredlcngth and point C is located
at its mid-length. DE is nextrct out perpendicular to BD and polnt
E is located so thatIt ls ln line wlth points A and C. If the
length of DE isrccurately measured, it should be equal to the
length ofthe regulred Line AB.11-3. ILLUSTRTTIIIE PROBLEI{S.l.
COHBIIIEO COnnECnOItS. A line wos determined ro be 2395.25 mwhon
meosured with 'o 30-m steel lope supported throughoul its
lengthundor o pull of 4kg onO ot o rn?on tmproture of 35oC.
Determine the cor-rcct length of tha line if tho ?op6 used ls of
stondord lngth ot ZOoCunder o pul.l of 5kg. The cross-soctionol oro
of the topi is O.O3 sqcm, its coeff icient of lineor erponsion ls
o.ooooll6/1"c. dnd the modu-lur of elosllclty of sleel ls 2.O x
106kq,/cm2.Glvcn:
t-
NL=9=
Solu lion:
2395.25 m30m4ks
T = 35'c A = o.o3cm2T. = ?o0c c =o.ooooll6/t'cF; = 5kg E = 2.a
xlo6kg/cm2
o) Ct = CL (T - Tr) = O.OOOOI16 (2395.25)(35 - 20)= + O,42 m
'(Corrcc?lon for lht moorur.d lcngth du. lo t.rip.rotur..
Thc porlliv. slgn lndlcot!r tiot top. h too long)hr . - (Pm-
P3)L - (4-5)2395.25et
-P - AE - o.og t2.o x 106)= - O,04 m (Corr.ctlon lor th.
m.orur.d lln. dur ?o l.nrion.Th. n.go-tlva rlgn lndlcol.r lhot tqp.
lt too rhorll
c) L, =LtCrtCp" 2595.63 m
2. COilONEO COnnECf lOIlS. A SO-m sleel tope is of stondord
lengthunder o pull of 5.5 kg whn supportod lhroughout its entiro
length. Tho
= 2395.25 + O.42 - O.O4(Lgngth ot mgosurod llng corr.ct.d fol
cft.cls of tompa-roturo ond pull)
,orlfi""r!trtf,,fl& ; I I L
-
top6 wclghs O.O5 kg,/m, hor o crosr-s.ctlonol or.o of
O.Orr_T,-i".liri,**iil;',r'itl'"'-Tir'rldlllTiiii,{:iirffi
iili458'650m. Ar the trmc rhe mcosurcmsnt. wos mooe, rn.'.on"ronr
guilopplled. wos I kg lt_r!..rhs
-rop" -!3neJiil'a iiiy';;-trt'oic polnr. orrrrmine ?he correct
tength of rhe 1lni.-
G ivan:NL=P3:ut=
'p!'m
Solutlon:
50m5.5 kgO.O5 kglm8ks
O.O4 cm2-2.lO x tfU,stcmz458.650 m
" O.ooOOil6 (459.65Otil8 -20)(Corrrctlon loi th. mrorurid tln.
du. tonrgotlvr. rign indicotor thot' topr j. too
l?:r_l:-"tlol. duo ro 3oe qT Og-,r,. spon. Th. .ff.c,
ot,o0orwoys molo thc topc too 3horr,
24r2{Co?r.ctlon dur to toe tor th. g.e6m rponl
l8'co.ooooil 6/toc458.650 m
A=F=l-:
o) cp = (Pm I-PJL= + O.Ol4m
_
(8 - 5.5) 458.650
O.O4(2.tO x tO0(Corr.cllon lor lho mcarurod llnc ducsltlvc rlgn
lndicoto, thof toOr tr toob) c. =_',rr'L: _ _ (o.o5f (5o)g
-r 24e;z 24 rcF= - O.2O3 m
_
.r,'aL3%--4 =-= - O.OOlm
Nolc: sinca lhare ora nlle 5_o--yt,spons ond one g.65m span in
moo-suring o totol dlstonca of 4Sg.650m.g(-ql)
- Cr2 = 9(-O. 2O3'l - O.OO1- L828m - (Totot corrootlon du. ro
toglL l Cp tCa = 458.650 + O.Ot4 - t.82g456.836m (Lrnerh ot
m.o!ur.d lin. corr.ct.d lor .ft.cr3 ot r.n.ion
ond .og)
(0.o5)a (8.65)3'
to l.nrlon. Tho porlong)
t.mp.rctutt. Tlt.horl)
cr=
c)Lt=
t cot?ltED coilnEcrtolls. rn probrem no.z,ft rhs ropo usod
wosstondordized ot 2o"c,ond durrng tne ireosurement-tne' m"--on
t"mp.rorureobserved wos r8oc, .derermine't-tre coiicct
rengih'oi'rne"riis for rhe com-
11111 "lf-"-"ls,o_f
reniion, so9, ono iemierq?uro. Assume rhe coefficrenr ofrrnoor
oxponsion of rhe rope to be equor to o.ooooil6 per r creg
c.6lven:
Cp - +O.Ol4mCa = -1.828mT3 = 2O"C
'Solutloa:
o) Cf : CL(T - T.)= -O.Ollm
, I I g_ i5iffiff,f,i"r"f,_'
T!
lg
!cr ' 458.66o .'l.o,o - 1.828 - o.oll.lL.nelh ct lhr rnoo.ur.d
llnr oorroot.d to? lh' oenblnrd'rtfoitr ol lonrionr .oer ond
l.nD.rolura)
a, nEAgunwo ANOLES Vt7H.7AP.E. The onsle P_e^twe6n
lwo-intsr-idoiir,e-lin"ej r" to-6"-aet"rmtnec wllh o l-oP' A polnt
on eoch fencellnr lr orlobllshed SO.O m f rom the poinl-of
interse'cllon. lf lhe dlslonceuli"i-.n-
in-,i'i-riiuriixii'i"ii.,il" ii"izliii'i", '"iii.ii, ile
tnrersedlon onele?Jlt, tt-tt
llL'ra
Polnt otlarrtcllon
Eolutioa:o) Delermining
Cos 4CAD
-
12-1. LEVELIIIG.Lcveltng ls the process of dtrectly or
indlrectly measurlngvertical aistanles-io a"t.tmine the elevation
of polnts orthelr differences in eLevation' It is a vital and
lmportantaspect of surveyi"g
"ince leveting operations are underta-
ken to provlde-nicessar'y data f6r Lngineering.design
andconstruction, ."J-in. priductiori of topographic napE' The
";;t;;;iilv Lt
" "it" ftrg development can be better deter-
mined by using in" resutts obtiined from levefing opera-tions.
Through in. pt"".sses of levelinE' buildings' roads'i;;ir, ana
6tn.i vlrtical and horlzontal structur,es can.bedesigned ana raLa
;;a-io tiest conform to the configurationof the ground.
L2-2. DBFIIIITION OF TBRHS.To better understand leveling
operations-' . fht
followingbasictermsaredefinedbelo',"n-dsomeofwhichareillus-trated
in Figure 12-1.
1. Level Surface. It is a curved surface which is atany point
perpendicular to the direction of gravity or the;i-;d rini. rt is
best represented by the surface of -aIarge body of still water'
However, a level surface is nota plane and does not have a regular
for-m because of localdeviations ot tne p}umb line. ro sorne ef
fect, t|re Qirectionof gravity depends on the distribution of the
nasses of theearthlscrust",,do,,-theirdensities.Suchthatifaplumbbob
is held vetiicalry at the base of a mountain, it
willhavethetenaencyto.deflecttowardthemountaln.Althoughthe
deflection woufa be small and negligible' nevertheleasit makes the
level surfase sIightly irregul'ar'
2. Level Line. A level line is-a curved line irp a
levelsurfaceallpointsofwhicharenormalto.thedirectionofgravity ana
equiaistant from the center of the earth
3. ttorizsntal Surface' It is a plane that is tangent to"
r"J"r"J"ii"""-"t a particular point' t!9 horizontal sur-face is
also perpendiculaE to the plumb line at the same
A straight line in a horizontala level iine at one Point'
Thisthe dlrection of gravitY at thethe mean radiuE of the earth
is
point.l. Horizontal Line.plane which is tangent to
Iine is PerPendicular topoint of tangencY.
SiPce:;il;t";i,rJiv'i".i", it is
-practical foT most purposes toassume that a tev6t'line and a
horizontal line are the same
line paralleI to the direction of gravity' It ls exempli-ii"a
'by the direction taken bv. a strl"?
":Plo:::i:-"-.. ::"-:irrr*i uol-p"""ing throus}t " point' For
ordinary pur-it i" conven'ient -to as.sume that the earth is a
truewith a smooth surfacer'and that a plumb line held at
for short distances.5. Vertical Line.
pendedposessphere
A vertical line at anY Point is
1 A 'EA'U.EIIN| OF.l 1+lt- t.Dlta4 otsr.dc6t ,,{f i|,t""if
l,',{'-J?5
\Fi4. tl-r.i.t/l,tionthlp be&., Itvd tnlantt.
any point on its surface is al.ways directed toward the cen-ter
of the s.phere.
6. l{ean Sea Level. Mean sea }evel is an inraginary sur-face of
the sea which is midway between high and 1ow tides.It is taken as
the reference surface to which most groundelevations. are referred.
This surface is determined by ave-raging the height of' the sea's
surface for aII its tidestages over a long'period of time which may
extend lo about20 years. Readings are usually taken at hourly
intervals onvarious properly distributed stations. Mean sea leveI
isnot a steady frame of reference due to the melting of icein the
polar regions, the effects of volcanic activity, andnnny other
influencing factors; It is for these reasonsthat it is/necessdry to
have a continuing observation ofsea leveI fluctuations to detect
changes. This surface,which is 'considered to be at zero elevation,
conforms tothe spheroidal shape of the earth and is perpendicular
tothe direction of gravity at every point.?. Datun. Datum is any
convenient level surface coinci-dent or parallel with mean sea
level to which elevations ofa particular area are referred.
.Any surface nay be used asa datum when relative elevations over
a limited area needsto be established. It is done by assigning an
assumedelevation to a reference point and determining the
eleva-tion of other points in the vicinity with regard to
thisvalue
8. Blevatlon. For a particular point, its elevation isthe
vertical. "distance above or bel.ow mean sea level or anyother
selected datum. Points on or near'the surfa-ce of theearth have
either positive or negative elevations, depend-ing if,the point is
above or below mean sea level.
9. Differenee in Elevation. The difference in elevationbetween
two points is the vertical distance between the twolevel. surfaces
in which the points 1ie.
-
L2-3. LBVBLITG IIBEHODS.There are valio,rt ,i"tnodg whtch could
be emgloyed to deter-mine the eLevatlon of points and their
differences ln ele-vation. These methods nalt be undertaken either
dlrectly orindirectly ln the fte1d. The princlpJ.e involved ln
eachmethod dllfer in some aspects. Also, they nay dlffer
vlthrcspect to the type of lnstruments used, the procedure
em-ployed, and the attalnable degrees of preclalon. Traditio-nal
methods of levellng have been used for so rnany yearsand they stiIl
continue to be useful in the present .tln9'such methods lncludel
dlrect leveling, trigonogfetric level-ing, and barometric leveling.
IConcurrent. with recent developnents in surveying ins-ituments,
newer and more prectse technlques have been deve-loped. gome of
these utilize el.ectronic instrumente such astolal geodetic
statlone, the airborne proflle recorder, 8a-tellite doppler
systerns, and lnertial surveylng systems' 1nthe following llssons
no attenpt will be made to discussthese new Leveting methods.
concentratlon-yl11 be rnade onlyon conventional and traditlonal
methods of levellng, thlgbetng an el.ementary course o.f st.udy in
surveying.
1. Dlrect or Splrlt Leve1lng. Direct leveling ls thecominon!.y
employed method of determining the. elevatlon ofpolnts some
dlstance aPart by a series of set ups of a le-veling instrument
along a selected route. Thls method oflevellng is also referred to
as spirit leveling since thedevice used ls a splrlt level.
Differential I'eveling, dou-ble:fgdd3d *l_eveJ!-gg, and tlr-ee-::tj
Lng are forms. ofaireEt Leve-fing. In direcf leveling vertlcal
distances aremeasured above or below a level llne and these.values
areused to compute the elevatlon of points or thelr differen-ces in
elevitlon. Being the most:.preclse nethod of levei.1 ing, it ts
used rrhen a htgh degree of accuracy is re-quired
2. ReclProcal Leveltng. Reciprocal levellng is the pro-ce6s of
accurately determinlng the difference in elevationbetween tvo
intervlsible polnta located at a considerabledlstance apart and
between vhich points leveling could notbe performed in thel usual
nranner. This method ls commonlyemployed when leveling across a
wide river, a deep raviner'or across canyons and gull.les where it
would be -dlfflcultor impossible to nraintain a foresight and a
backsl.ght dis-tance of nearly egual lengths. Reciprocal levellng
providesa faster nrethod of determining dlfferences in elevation
andwhen it ls carefully conducted, it could be as precise asdirect
Leveling. In determtning the dlfference in elevatlonbetween the two
points, it will require two setE of obser-'vations and the mean of
whlch, is used. Sinee there ls ine-quality between the sights
taken, the plocess of recipro-cal, leveling ls expected to
elimlnate the errprs resultingfrom crirvature of the earth and the
refraction of the at-
,)26- ffifi{ff1i&ff c,
mosphere, provlded that atmospherlc condltlons do notchange
durlng the process of Iev-Iing.
3. Profllc Lcvellng. This method of leveling ls used todetermlne
dlfferences in elevation between points at desig-nated short
measured intervals along an established line toprovlde data from
whtch a verttcal section of the groundsurface can be plotted. In
the deslgn of roads, railioads,canals, dralnage 6ystema, and
transmission Ilnes, it Is ne-ceasary to flrst obtaln a profile of
the existlng groundsurface.. I't lE this'method of leveltng which
yill best suitsuch requirements.
l. Trlgonoretric Leveling. Thls method of level.ing ,lsemployed
1n determining by trlgonometric computations thedifference ,in
elevation between two points from measure-ments of its horlzontal
or slope distance and the verticalangle betyeen the points. The
reguired distances.are usual-ly obtained by stadia, triangulation,
or by direct taping.By most leveling standards, trigonometric
leveling onlyprovides a very rough deterninatlon of dlfferences in
eIe-vation. Its degree of precision may be improved by usingprecise
measuring instruments such as optical theodolitesand total geodetlc
statlons which measure angles to 6e-conds. However, there are
certain occasior,"
"udh a. in map-ping or surveying ovef very rugged terrain when
it rrould befully Justified to undertake trigonometric leveIing.
.It tsalso a convenient'method to adapt when it is required onlyto
determ.r-ne the elevation. of principal stations or
con-ttttultlliii" Levettng. stadia revering combines featuresof
direct leveling with those of trigonometrlc leveling.This method is
in fact a form of trigonometric leveling. Itcan provide, reasonable
accuracy for preliminary surveys,napping, and r,ough leveling,
where quisl neasuremeBts areneeded. In stadia leveling, differences
ln elevatlon bet-ween polnts are computed from observed vertlcal
angles andthe three lntercepts on a rod held. at each potnt
backs"ight-ed or foreslghted. Any surveylng lnstrument rnay be
employedin stadia leveling as long as lt has a telescope to
readvertical angles and is equipped with stadia hairs in addi-tion
to the standard cross hairs.6. Baroretric Leveling. Barometric
leveling involvesthe determination of differenees in elevation
betweenpoints by'measuring the variation ln atmospheric pressureat
each point by means of a barometer. Thts leveling methoddepends on
the basic princlple that differences in eleva-tlon are progortionaf
to the differences in atmosphericpressure. The readings of a
badqmeter at differ.ent pointson the earthrs surface provides a
measure of the relativeelevations of these points. It is an
accepted fact that thepressure 'caused by the weight of 'a column
of air above theobserver decreases as the observer goes higher in
altitude.The method is. particularly useful for lorr precision
level-lng over rough terrain yhere extensive areas need to be
olfilt [Elllo?I
-l3z
-
covered and dlfferenceg ln elevation are large. It
lsprlncipall.y employed on reconnalssance surveya or otherwork
requiring only approxlrnate values. However, lt ls notdesirable to
employ when the atmospheric pressure in thearea changes
rapidly.
7. Cross-Section Level.lng. In hlghway or raitroad
cons-tructions it is often necessary to obtain a representationof
.the groupd surfac,e on elther side of the centerline.
"Short profiles at right angles to the line of work areusually
plotted at regular intervals for this purpose. Thtstype of data'is
obtalned in the field by a precess referredto as cross-section
leveling.8. BorrorPit Leve1ing. Borrow-pit leveling is a methodof
determining the relative elevations of points in borrow-pit
excavations for the purpose of calculating volumes ofearthwork.
This type of nork is usually encountered in theconstruction of
roads and railroads.L2-1. TTPBS OF LBVELSThere are various types of
instruments. used in levelingjwerk, the basic instrument used,
however, is the spirit le-vel. Other instrumeirts employed in
leveling work includethe hand leveI, alidade, translt, theodolite,
aneroid baro-meter, and EDM instruments. Although these instruments
maydiffer somewhaL in design, each can be used to establish
ahorizontal line of sight by means of a tel.escope fittedwith a set
of cross hairs and a level bubble.Fig. ll-2. tutry1 ltvt.
l
ItA tE.tuuEJEflr ofrrLv- tEnncaL ottfatcet
l. DurBy Lcvcl. The dumpy level (FIg. L2-21 Ig the mostwldely
uEed dlrect levellng lnstrument. It has a long te-leacope whlch is
rigldly attached to the leveL bar. Theteleacope, which can be
rotated through 350 degrees, fixegthe direction of the line of
sight. Attached to the levelbar is a 1evel vial which always
rernaing in the same verti-cal plane as the telescope. A leveling
head supports theteLescope and permits the bubble in the tube to be
centeredby means of the Ieveling screws. The whole. instrument is
inturn supported by neans of a tripod.
The dumpy level is simple in construction. Its mainparts are all
made in one casting which are fastened rigid-Iy together. Since
therb are only a few moving parts whichcould be worn out or
displaced, the irlstrument requizesfewer adjustments.
2. Uye Level. The wye level (Fig. L2-3') is very. identi-cal to
the dumpy level. The only distinct.difference bet-Fig, l2-3. 9e
bvcL.
Lav.l Vlol Focualnc xnob D.tochobla lalarcoPr
Coprtcn - xoodaa ScrarCllrt
Wtt Sug9otl Yra Sugpotl
Crorr AorTtlarcopa ClomD
L.v.llnf Scr.:
Eool Plol.
loaganl Scr.r
Trlgod l.rgr
neen these two lnstruments is in the manner by which
theirtelescopes are attached to the supporting leveI bar. Thewye,
level has a detachable telescope which rests in sup-[rorts called
wyes. It can be removed from the Y-shapedsupports pnd turned end
for end during adjustment by relea-slng the two clamping collars
which fit across the tops 'of
,,!,'ii!"i i!',n&
-
I 29,
-
the Yrg. curved crlps are used to facten the tcrcacopc
lnplaceThe wye level iE non almogt obEo],ete and acldomly uscdsince
newer levels are better congtructed and satlsfactoryfor most
Leveling work. Although this Leveltng lnstrunenl
was not as popular as the other revels, many of lts' oldermodels
have more sensitive bubbre tubes than the othertypes of engineerrs
level.3- Buirderrs Lever. This inEtrunent is used prirnarrryin the
different phases of bqilding ionstruction where Ihigh degree of
precision is not a prlmary requislte. En_gineers, architects, and
builders use it in the settlng ofcqncrete forms, batter boards, and
tn establlshlng gridesfor earthwork.Fi4. ,2-1. &ildtt't
bve!.
It is often called a construction Level or an archl-tectts
level. The level. vlal is not as sensltive as inother levels and
lts telescope haE a lrch lesser magnlfyingporrer. The horizontal
circle, which is found between thelevel vial and the leveling head,
is its special feature.This circle ls used when measurlng or laying
out horizontalangles
,1. Autonatic Level. Self-Leveling features are incorpo-rated ln
automatic levels. This type of 1evel has becomepopuLar for
conventional leveling work because of the easeand speed of their
operation. It does not use a level vialand lts abillty to Level.
ltself depends upon.the actlon ofa complex pendulum-and-prlsm
device.An automatic level is equipgrcd with a prismatic
devlcecalled a compensator yrhich is suspended on fine,
non-nlgne-tic wires. l{hen the instrument is approximately centered
bymeans of a bullrs-eye'Ievel, the force of grlvity on
th;compensator alLows the optical system to swlng into a posi-tion
which wiLL autotnaticat ly rnake the line of sight hori-zontal. The
line of sight renains horizontal as long as thecircular bubble
remains approximately centered.l?,n alatueEtElt cUIZ:U.I vc?rtctL
otstaicEt
"\Flg. ,l-t. ,ttanl.ac &,ve/..
1 The level is not affected by any slight novement orsettlement
which wouLd disturb the bubble or Iine of sight.Its pendulum actlon
autornatically shifts to maintain atruly horizontal 1lne of sighf
whenever the instrument isslightly disturb. This type of Leveling
instrument is par-ticularly useful where the ground is soft or
rrhen strongwinds blow agalnst the instrument since it can
autornatical-Iy relevel itself
Fig. l2-7. giH gadetie tavat,2-6. Uitt ilning lzva, *ith
tstalahlt&leu.on d rcvuaihil2 ttthia.q. Izvet.Fis.
,e!,'ii!,fE1IL,%
-
l3l ,
-
r5. Tllttng Levelg. ,Thls type of levellng lrlgtrument(F19.
12-5) can be tilted or rotated about lts horlzontal
axis. A bulI's-eye level is employed for its guick
andapproximate ,leveling. The tilting knob is used to rotatethe
telescope into a correct horizontal positlon. Tiltlnglevels are
cotnmonly employed for very precise levellngoperations and in other
general leveling worl. It ls a'Isoequipped with a horizontal eircle
which rnakes lt suitablefor layout and construction surveys.
5. Geodetic Level. The geodetic level is basicaLly ano-ther type
of tilting level. Most of its metal parts aremade of invar to
reduce the effects of temperature. Geode-tic levels (Fig. L2-7 )
are.employed in first-order levelingwork where extreme precision is
an important
_requirement.The instrument is equipped with stadia hairs ih
addition tothe standard vertical and horlzontal cross halrs to nake
itsuitable for three-wlre leveIlng. .llhen uslng the lnstrurnentthe
obqerver has.to stand erect since it is designed with ahlgh tripod
to bring the line of s19ht way above any inter-vening ground
surface. This was purposely done to lessenthe effects of
differential refraction of extra long llnesof sight.
?. Translt as a Level. The engineerrs translt has al-ways been
referred to as the ttuniversal surveying lnstru-mentrr because of
its variety of uses. There is no doubtthat it can also be used for
leveling work. It can prdvlderesults which are fairly precise
although not as good asthose obtained with conventional levels.
This is becausethe transit has a relatively shorte.r telescope and
1ev91vial.
Fig. ,2-t. uiLd N 2 convc tcd to a. It^u.Iuel uing a GUz ItAl
egepic-ct. Fag. l2-9. La.u a!.ttn rasrtal or-o'.lzvgllng
it^t^un,rrt.
8. Laser Level. A new innovation introduced to aurvey-ing
operations is the use of lasers. A laser system ls aseparate unit
equipped with a portable power supply and naybe 'a hellum-neon
laser or gas laser. They are usuallymounted or attached to
conve4tional. surveylng instrumentssuch as leve1s, transits, and
theqdolltes. The Wlld NA2
l7o aEtsutarEtr *, r vc- vErllctL gt5rttcE
(Flg. 12-8) wtth an attached laacr eycplece la an cxamplcof i
Laser convertcd lavcl. The eyeplece lncludes a spectalretlcle yhlch
hag a snall free spot ln lts center to allovthe laser llght beam to
pass freely. surveylng lnstrumentsvlth laser attachments are
1dea1,ly sulted for appllcatlonsln levellng work, bullding
constructlon and layout, and lnmany other englneerlng activitles
wher.e reference lineghave to be establlshed accurately.
Laser llght is a low-powered bea.m of red l, 19ht which
lssultable for projectlng a llne of slght since lt is cohe-rent and
hlghly colllmated. A sharply deflned llght spot lsfocused at the
target when the telescope lmage ls focused.The laEer beam.can be
proJected along an optically stralghtpath and lt spreads only very
sllghtly as the distance fromtfre Eource to target lncreases.
Projected ls a vislbletrstrlng
.1 lnerr beam whtch can be seen on targets under dlf-ferent
lightlng condittons. The rnaximum range of the laserdepends on
aimospheric condttlons and thc nature of thetaiget surface. During
dayllght the range is about 300 mand at nlghtlrne lt ls about 600
m.FiS. lt-rl. Litut 4.t2n put*n ot a hildet't lzvo/.
hand level. (Flg. 12-11) is a hand-The9. Hend Level.rEtsutEtEtr
il I aa
vznftcaL ot'f.*cEs rc
-
hcld lnstrument ugcd on lurveyc rnvolvrng rhort atghte andvhere
a row order of.accuracy ra suff'lclJni.--rt n", bccnproven to be
ugeful 1n reconnalssance r"i"ay", tn cro!3-sectlonlng to obtaln
additlonal ,o9 -r."airri"' on al.optngground' and ln taplng to
determrne rf trr.-t-ip" rs herd ho-rizontally during rneasurement.
Thls instrumint atso pro-vides a quick qi o5 o"t.i'lii"s-;;;
ii;;'ll=iio, row thaengineer'|s level should be set up tn oia"i-to
u. iui.read a leveling rod held a certain-Oirti"".
"rly.Fig. ,l-rt. ,tard txieI.
The hand lever' consrsts of a brass tube about 15 cmlong having
a plain glass objectlve_anA i-p".p sight eye_piece' on top of the
tube is a snalr revel viar refrecti.ngthrough a pri:I which appears
to move vertlcally whenviewed through tne eyeSireci. when the
'uuuui"'-"ppears to beon the cro6s line it is in the center of the
tube and ahorizontal line extends across the hand i;";i.; Durlng
reve-ling, the instrument is held in one nana iii r.evered
byraising or louering the oUjecttve end uniti--ifr" crose
linebisects 'the bubbre. ro obtain a steiot ;;;h;; ir may beherd
beside a vertrcar staff or by uringrrif-rt close toone16 cheekbone.
The user of a hand level-i"i." a backsightor foresight on a rod
whrle standrng in-one---positron andthen moves ahead. to repeat the
process. The.re is no magnl_f ication by the hand r.iver and il.
i"nettr-oi-s-ignt is linri-ted by the vtslbirity of rod readinEs
ising-tne naked eye.The use of a hand revel courd piovrde i.""it"
wlth suf-f.'cient accuracy and it is rnore convenient and rapid to
usethan the englneerrs level. They are designed to stand upunder
rough usage and do not require freguent adjustmentbelng simpre in
constructron. Th; nana revei-irlir"--;;:tremely useful in different
phases of construetion such aEin excavationsr...setting.of grades f
or curbs ;il-- ;;;;"r;;and in checkins the posiiioniig ot
t.irr"ii-Ioi tr," pourrngof concrete.
l7d nEatuntEfrt 6!..!- yErftc& OtStatCES
Lessott lr'",
ii| it' E i!'#, "T,
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I 35.
IilEASUREITENTOF YENTICALDISTANCESI3-1. LEVELII'G RO'S
l. Srll-Retding Rod2. tatget ?od
,3-2. on{rjt Ty?es oF R00l. Rotu Nand Alte,2. Rod Ribboru3.
Pr.rtite Rod1. @odetlc Rod.5.. Tape. Rod.
t3-3. k00 LEuELt3-4. TARqETSt 3-5.
_
TEt ESCoPES
l. 0bjettive Le:u2. Egepiete3\ ?s"ou lta,ira
t3-5. 'IAGNIFICATT0ilt3-7. LEVEL.VTAL
I 3-t. eollrcIoEt/f;E 8{rE8r.Et3-9. TRLPfiQS
Citiu on Statet
-
13-1. LBI'ELITIG BOD8.A. lPveling rod ls a graduated rod which
ls used for measu-rtng the vertlcal distance between the 11ne of
slghtthr6ugh d 1eveling instrument and the potnt whose elevatlon'is
ei{her required or known. Rods are made of wood, flber-gLass, or
metal and have graduations in meters and declnalswnrcrr'start from
zero at the bottom and extendlng upvard toIengths of 3 or 4 meters.
Wooden tods are rnade from select-ed stralght graln, hard wood,
carefully sanded and treatedwlth a preservatlve staln that reElgts
moisture.absorptlon.The endi of the rod are protected by a hard
metal. shoes andcap6. A wide cholce of colors, gatterns, and
gradubtlonE isavitlable. Some are nade 1n one, two, or thrAe
sectlons andm.ly be either telescoping ot hlnged for ease_ln
transpor-ting. Most levellng rods have convenlently deslgned
pat-terns whlch allow readlngs to be taken eaaily and vith
lesschance of commlttlng mlstakes. Levellng rods rnay be eltherof
the follovlng:
1. Self-Readlng Rod. Thls. ls the most comnonly usedtype of
levellng rod. It can be read directl.y by the ins-trumentman
through the telescope by noting the apparent in-tersection of the
horlzontal halr on the rod.
2. Target Bod. Thls type of rod has a slldlng targetwhich is set
and read by a rodman at the posltlon sel'ectedby the
lnstrumentman.It can be expected that results obtalned by reading
the roddlrectly is practlcally as accurate as that done by
readlngthe rod with the atd of a target. Under favorable
condl-tlons, leveling rods are readable through the telescope
fordlstances up to about 90 meters frorn the lnstrument. A tar-get
should be used when longer dlstances are lnvolved. Thetarget is
extrernely useful shen readings are taken in dlm-ltghted areas, In
dense vegetatlon, and when establlshlngseveral points on the same
straight grade llne.Lt-2. OTHEN. TTPBS OF ROD.There are Eeveral
other types of rod used ln leveling work.Arnong these are:
1. Rods Nand tfter Ctttes or Stateg. Levellng rodgnamed after
citles or states include the PhlladelphiatDebroit, Chicago,
Florida, Boston, New York, Troy, and SanFrancisco rods.
The Philadetphia rod (Fig. 13-1) ls a comblnatlon self-readlng
and target rod and ls the commonly used type ofrod. It ls made in
two sections in vhlch the rear aectlonslldes over the front
sectlon. Readlngs less than tuometers are taken uslng the rear
sectlon of the rod and lsreferred to as readlngs on the short rod.
For readlngs bet-lza tatrurcactr oaI rvv- fJrttcaL orsfatcat
Fis. t3-1. Philade2dtia. todt.lliptlcol Torg.l(Motol Plor.)
ncd
ClompScrawJ Tor0ol
Clonp
BrosrSloovot
tbllbtti.c. Gtfu.tion
lclEng/-i,th @ufutionlalEqliA Gnnilnlion
rlilit'Effi:,:E
-.192,
-
rreen two and four meters, the long (or hlgh) rod ls used
byfully extending the rear section.
The' zero mark is at the bottom of the rod and the gra-duations
extend upward to usually four meters. Red colorednumbers are used
to portray the full meter marks on theface of the rod. Black
numbers are used for tenths, and thehundredths are shown by
alternate black and white horizon-taf bars. The graduations on the
rod are continuous whenthe rod is fully extended. The Philadelphia
rod can be readaccurately with a leveLing instrument ai distanges
"uP to 90meters. For much longer distances a target shbuld be
used.
The Chicago rod comes in three sliding Eections "ld,usually
extends to either three or four. meters' It iEgraduated . similar
to 'the Philadelphia rod except that ,t.1"
iig,rr." on the face of the rod are wider and thus more
sui-taute for longer-distances. . The rod is designed to be
col-lapsible for ease in transporting. This type of rod iswidely
used in construction'surveys.
2-. Rod Ribbons. This is an improvised type of rod usedin
leveling work. The graduations on this rod. are
-markedeither on canvass or metal strlps. whtch are attached to
along piece of selected lumber by staples. Rod ri.bbons arequiie
nandy as these can be easily removed from the wood to,ni"n it is
attached, rolIed, and put into oners pocketafter it is used. since
rod ribbons can be'easily comparedwith a standardized tape before
it is used., they are suffi-ciently Precise for ordinary leveling
operations'3. Freclse Rod. The plecise rbd is a f,orm of rod
rib-bon vhich uses a graduated invar strip permanently fastenedto a
four-meter long wooden or metal .frame. It is eguippedwith a rod
level to alLow the rodnan to hold the rod verti-caLly when used.
For. precise leveIing work'a thermometer isattalhed to it for
purposes of reading the air temperature.
l. Geodetlc Bod. This rod is similar to a preclse rod,except
that a nilvar metal strip is used instead of invar.Nilvir is an
al1oy of. metal with a very low coefficlent oflinear expansion. The
graduations on a geodetlc rod arepalnted upiiae down fo,r use with
inverting telescopes, andare shown in meters, decimeters, and
centimeters.- 5. Tape Rod. This seldomly used rod is also known
asthe automatic rod. Jt iE used advantageously when
numerouselevations are to be'..determlned from a single set-up of
theJ.eveling instrument. lfhen empl'oyed in Ieveling work, the
' tape rod elimlnates the need to add backsight readings
todelermine the height of instrument or to subtract
.foresightreadlngs to determine the elevation of sighted points
Th; tape rod is useful in profile leveling, in takingcross
sections, and for the different phases involved inbuilding
construction and layout. A three-meter long gra-duated metal tape
is looped.around the frame of the rod bymeans of rollers located at
uottr ends of the frame. Thetape can be rotated or fixed
temporarily in any positionfor a sequence of de_sired rod readings.
Harks inscribed on
Jlg- ffifi[ii|ihlicn
Ene rod are slmilar to those used in'Phil.adelphia rodsexcept
that graduations increase downward. -
'To illustrate. the use of this rod, assume that a taperod is
held vertically on a poi-nt whose elevation is L23.45meters. The
rodman then rotates thertape around the frameuntil the line of
sight of the leveling instrument falls on3.45 m. The tape is then
clamped into this position. Therod is next moved to a point whose
elevation is to bedetermined. A rod reading on the point of, say
2,86 m meansan elevation of J.22.85 m; f or 3.0? m the .recorded
elevationts 123.07 m; for 1.98 m the recorded elevation is L21.98
m;etc. The foresight readlngs on the rod gives elevations di-rectly
and eliminates the need to perform subtraction,until the
instrume.nt is moved to another set-up. Shouldthere be a need to
transfer the instrument to another loca-tlon, the clamps of the rod
erre released and the tape loopIs reset. This is done by again
sighting on a point afknown elevation. The process of determining
elevations o.fforesighted points is continuecl in a similar manner
as ear-I ier explained.
I3-3. ROD LE!'EL.The rod level (Fig. 13-2) is a deviceused for
fast and correct plumbing of aIeveling rod. It is t-shape in
design'andcohsists of a srna1I circular spirit levelfastened'to the
rod or to a small bracketheld against the side of the rod. llhenthe
bull's-eye bubble is centered, therod is plumb or correctly held
vertical.A different type consists o'f a hingedcasting on each
wing. It is mounted on aIevel tube and held parallel to the faceof
the rod. The rod is plunb when both ofthe bubbles are
centered.13-{,. TARGBTSA target is a small device attached tothe
rod when extremely long sights rnakedirect readinE of the rod
difficult orlmposslble. Targets are made of metal and
flg. l3-2. P.od lzvil.
may be circular, e1liptical, or rectangular inzontal. and
vertical lines are formed by thealternating red and white quadrants
painted onusual"ly has a'rectangular opening in the frontportion of
the rod in order Llrat readings cansmal1 vernier may be attached to
the target toaccurate readings on the rod.
Targets are used not only on extrmg1y long sights, butalso when
the rod is held in poorly )ighted places, whereatmospheric
conditions may cause adverse effects on rea-
shape. Hori-junction ofits face. Itto expose a
be made. Aallow more
,, i,l ltrf ii'/IL 3!',
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I 3.9
-
Fig. l3-3. fltiptical *tal ta'aget'
Fig. l3-1. 0the.t' lotnrr of, tatgett.
r Op.nlng
Whii. Point.dOuodronl
R.d PointodO uodront
ato
dlng a rod accurately. They are also ::ed yhen vegetationor
othe! obstruction; to a tine of slght make the readlngdlfflcult t
oE rrhen setttng a llne of stakes at the sameelevatlon. tne target
ls moved up or down under the direc-tlon of. the Instruirentman
untlf ft app93r9 to be bisectedUy-[n"-.io", nafis, but lt ls.
r+ad-b1r-the rodman. Shown lnrigot. 13-4 are otirer forms of
targets used on rods'
ffi(c)@
13-5. TBLBSCOPES.The telescoPe of acontaining a systemtr19'; I E
i I iif,' 5 i!, li "'
surveYlng instrument lsof lenses which are used
metal tubeflx the dl-
rectlon of the llne of slght and ln nagnifying the apparentsize
of objects in lts field of view. A Dutchman, JanLippershey,
ltnvented the first telescope in 1608. The greatmathematician
Johannes Kepler was the one who suggested howthe telescope could be
employed for use in surveying ins-truments. This Led to the
devel.opment of the Keplerian orastronornical telescope which
consists of a tube with varia-ble length which has an objective
lens, cross wlres, and aneyepiece.F ig. I 3-5. l*ttrcnnical
teteJ:opc.t.
dust cop
Irte ruL Foctrtittg Telzu.oP.
Erte^nat F oetting T ele-x.opo.
In some telescopes the objective lens is mounted on agleeve
which moves back and forth in the telescope barrelaa an object is
brought into fdcus. This ls called externalfocusing. Internal
focusing telescopes have an additional'auxiliary lens which
movesrback and forth between theobJective and the cross hairs as
the focusing dcrew isturned. Both types of tel,escope are
illustrated in Figure13-5.
l. ObJectlve Lens. It is a compound lens composed ofcrown and
flint glass mounted in fh"e objective end of thetelescope and has
its optical axiF concentric with the tubeaxis. The function of the
objective lens is to allow liqhtrays to enter'the telescope and
form an image of the objectsighted within its field of view.
2. Byepiece. The eyepiece is a form of microscope con-taining
either two or four lenses and is used to enlargealtogether the
image and the cross hairs. It allows theInstrumentman to sight and
read accurately'the graduationson a leveling rod. Leveling
instruments may have either anerecting or 'inverting eyepiece
depending on the ar.rangementof the lenses. Each type of eyepiece
has a focusing move-ment ao that lt can be focused on the image to
suit each
ttttuettr|| or I Al..vtaftc.L ottratclS
-r
rt,a
-
Ilndlvldual eye7 'An eiecting eyepiece consists of four lenses
whtch both
magnify and erect the lrnage. Thls type of eyePtece ls
PoPu-1arly used slnce it allows slghted lringes to be observedright
side up. The lnverting eyepiece is another type whlchhas only two
lenses. It can only miignify the lrnage but noterect it. Although
the observer sees the lrrage upslde down,it is clearer and better
illuminated'since a lesEer amountof light is absorb by the two
lenses. The lnvertlng eye-piece is supe,rior in its optlcal
properties and is grefer-red by most engtneers and surveyors. l{ost
preclse I'eveIsernploy invertlng eyepleces.
3. Cross 'Hairs. The cross hairs (Fig. 13-51 conslstsof a pair
of lines whtch are Perpendicular to .each otherand are used to
define the instrument's line of sight. Theyare mounted on a reticle
or cross hair rlng near the eye-piece of the telescope and located
at tne princlp4l focuSof the objective optical system. It is flxed
into posltlonby ,two pairs of capstan screws placed at rlght,
angles toeach other. These screus are also used to adjust the
posl-tlonlng of the cross halrs. In telescopes of older'surve-ying
instruments, cross hairs were made of splder web orfine filaments
of blatlnum wlre. Some are $ade of fineglass threads and others
have a glass diaphragn on whlchltnes are etched. The dtsadvantage
of spider threads isthat they slacken when noist and reqpire some
skill tomount with Just the rlght amount of tensionFig. l3-5. Uou
hrit ring ott ,,etielt.
uPPcrHo ir
Tola!copoTubc
Hor lzonlolHolr
Crocr
Cross
Stod io
In newer lnstruments, cross hairs are ruled and etchedon a thin
glass plate, with dark metal filaments depositedto make the lines
visible. Cross hatrs mounted on glaseal,so have a disadvantage
since it cauEes a slight loss oflight and al1ows dust to collect on
the glass vhich fogsthe image. llost levels used for ordinary
leveling uork onl'y,t42- iiitilft|illi*
a
VerticolHoir
\\l|
jlg. ,t-1. OtlRt rl'ttcttu uxtl 6ott (tou ta.ira attd.tadit
ha,att.
hevd one horizontal and one vertlcal hair. Instruments usedtor
precise,, Ieveling have two additional horizontal hairscrIled
stadia hairs. Stadia hairs are shorter, are paraIIelto and
equidistant from the horizontal. hair. One of thertadia hairs is
positioned above the horizontal hair andthc other ls positioned
below. Various patterns of crosshrlrs and stadia hairs are used.
Some of these are 111us-trated in Figure 13-7.I3-5.
I{AGNIFICATION.Thc magnification of a telescope is the ratio of the
appa=rsnt size of an object viewed through a telescoPe to itstlze
as seen by tle uriaided eye from the same distance. Itnrry also be
taken as the.amount by which an object is in-crcased in aBparent
size. The amount of magniflcation isflxed by the ratio of the focal
length of the objective andthc eyepiece lenses. Magnification is
expressed in terms ofdlameters. For mos! leveIs, the magnification
may vary from25 to 40 diameters. Hlgh magnification,is not always
an ad-vantage since it limits the field of view of the telescopeand
reducds the brightness or illumination of the. viewedobJects.I3-7.
LBY'BL VIIL.A level. vi.al ( Fig. 13-8 ) is a sealed graduated
glass tubecontilnlng some amount of liquid and a small air bubble.
Itlc used to determine the directlon of gravity. The type ofItquld
used must have a low viscosity and freezing point.It mugt be able
to move quickly with very slight shlfting
wift',t'ii'ilffi
-.1{Il
-
ortlltlngofthevlalrandshouldberelatlvelystable-lnlength under
norlmal variations in temperalure. Alcohol
mix-edwithetherrandpentanehydrocarbonswerepopuJ'arlyusedearlier.
Xewiy designed I'evel vials now use purified'syn-
' thetlc alcohol.Fig. 13.t. Level vial.
AdjurtlngSaratv
Uniformly spaced graduations, about 2 mm long' etchedon the
tubE's-surfaJe locate the bubblers relative posi-tion. When the
liquid drops to the lower part of the vlal'inr
"ttt"pped air 6ubble mot.s to the highest point in the
tube. A line tangent to the top center of the bubble is
ahorlzontal line which is perpendicular to a plumb line' Theline of
sight of the telescope is sald to be horizontalwhen the UuUUte ls
located at Lne center of the graduationson the tube.Fig. l3-9.
Coincidence hrbbll.
o aAppeoroncc ofDlroclion Tokon
Bubblcs Ecforc C.ntorlng ondln.Turnlng th. L.v.ling Sor.w3.
App.oronco of Bubbla rh.n Ccnl.rad
(c)
13.8. COINCIDBNCE BUBBLBThis type of bubbte is used on most
modern and precise lns-trumenli such as the tilting and automatic
levels' It em?ploys' an optical device which splits the bubble
longitudl-nally, then turns one end around to make it appear
adjacent'totheotherend.lfhenthetgoendsformasmoothcurvG,ni"n
apparently-'Iooks llke the tlp of a hot dog, the bubblr
,I44- iiifillfth."k,'
eoled Glocsub. (groduotodl
Adj u!tingScrcY,
1s correspondingly centetedhtith the use of a coincidence
bubble, the set u'p and
Ieveling of an instrument can be rnade more accurately thanby
means of the conventional level vlal. The use of a cgin-cldence
bubble, however, has a dlsadvantage slnce lt is nottluays clear
which way the leveL needs to be tllted tobrlng the lnaggs
together.
f ig. 13-10. Tgpe-t ol tl.ipodt.
lclFixcr'-Leg Ttipd
lblExtttuion Tti+od
Aluminum
l3-9. TRTPODS.Trlpods serve as a base to prevent movement of the
instru-ncnt after It ls set up. A trlpod conslsts of three woodenor
aluminum Legs which are securely fastened to the tripodhead by
means of a hinged Jotnt. The legs are spread widecnough to provlde
a stable platform for the instrument.then settlng up tt is good
practiee to center and level thelngtrument flrst by adJusting the
trlpod legs. If the leve-Ilng head is establlshed nearly horlzontal
by means of thetrtpod, only a minimum of shiftlng and adjustment
with theIevellng screws would be necessary.
Tvo types of tripod are used with a leveling instru-mcnt. A
trlpod rrhose legs are made of a solld piece of woodlg catled a
flxed-leg (or hlgh) tripod. If the legs have arlldlng sectlon 1t 1s
called an extension trlpod. The
",
1,122t'5lr',*t%
-
| 49,
-
d ls more rtsld. and FI":-l:--Pot:l?:" .::;::;:-i;: r;;;';i
"igni llenei lboy: _!l:-:::":1;--lll'^. ':;:;::' ::;'i;'i;";iv-
;;;'.;;;;t- oi- it'o'ph:i l:-::I'?lj t,?l: ?l
.?il!'l.xJl-il;;;--;"-"it"""io" t.lpod is suitable' for use tn-t
r..-la,ll {.A:::n;"fi;.'il,,"!.t-;e;-;!;;i-tn'-i-esi "eea to be
adrusted tqiit'lni-.-nflguratlon of the ground'At each end of a
ttipod is iiiacned a. polntgd ?it::--:I
*"t"i' I"'iI.E"'"""n1":--;;; ;;.4;-ot tn. titpoa are forced^!
trarr:1 I glill'.n!'n'ii'u-oi';;;epi;; l; l:. :i:!-'1:l:.
I:ot;'-u'::lll:::; ":;.3"ilfJ'."ip;;-;fii;; ii'iiii"tes pushi.ns
-:n:--?"ll:?ll
"
.''i l= "'jl-.'l "-' ;- ;'
"
; ; ; ;' - t l' l- d e e p 1 v : l: : ?l- " :.,: :" t- :
l:'#J;'ir'il'=iil'J.iir5-JJi."l"iri-'r'"i sertins over softor
unsta!,l'e ground.
J46- iliffifSilu%o,,Lessott 14
-,, it trlt'fffiliafl
-
l -{Z
II]EASUNEIilENTOF YENTICAL
.IIISTANCESI'-'. SETTINE UP Tl'lE LEVELI'-2. LEVELIIrc THE
II'$XUTEilT
l. lndtnmrtt Uith Foutt Leve/ing Y)Leua2. lttttrtunt/-a Uith
Ttnee Leveling *tetu
la-t. ,t0Lollrc T,E LevELlltG 200la-l. TAX7jG A k00 PEA9rtrc
l. Potition The Rd2. F;st^ 0n Tte Rod3. Retd Tlrc ?,od
I'-5. OETEFI{INIITC OTFFEIEIreE TN ELEVXNON[Et,GfflS 0F
SIC'$|u$vnt} TrE, knclrfuvilrc TrE 7JsrRum{rAil AilD
"
lO SrGlrA[sl. lbve P,ig/ltr. at Le[t2. Give a Sightt. AIL
Risrrt1. Thia ia a Poirt5. lbve knk 13. Fase The Rod6. Pieh. Up
Intttunnb 14. Revenae The R'od7. lnile lot Lotps.l TatgQf. 15. lbve
fotw^dl. Cm. ln 16. lt6e The Long Rad
l1-5.tl-t.la-t.l1-e.
9. P'ttt* the Rod10. E&tahliah a Tutrhg ?oirt,1. ThU i,* a
Twtning Poirt12. lhve The Rod
-
1'-1. SBTTING T'P THB LEYTL.The leveling instrument may be set
up at any suitable ordesired location. When starting a Lbveling
operation theinstrumentman should first consider where he intends
toposition the instrument. The level is then puIled out froits box
by holding the. leve1 bar or base plate and screrredsecurely onto
the tripod head. Care should be exercised inscrewing the leve1. The
instrument'should fit snugly andbear firmly. If loosely fitted, the
instruinent will wobbleand be unstable; if too tight due to
excessive pressure, itwould be difficult to unscrew the instrument
later and rrEycause some damage.Solid ground should be selected
when setting up theinstrument. Muddy and wet areas should be
avoided as theseare unstable to stand on and may only cause serious
errorsin leveling work. Tripod legs are spread so that the
footplate will be approximately horizontal,. It will be easierand
quicker to level the instrument later if ttre pJ-ate isalready
horizontally positioned. The legs should be farenough apart fdr a
rigid set up, and they shoul.d be pushedfirmLy into the ground to
make it stand stable. The instru-mentman should see to it that the
telescope is at a conve-nient height for sighting and he must be
able to standcomfbrtably between the tripod legs. A preferable'and
con-venient height of setup is one which will enable the
ins-trumentman to sight through the telescope without having
tostretch or stoop. !
llhen setting up the instrument on hillsides or along aslope,
one of its legs shoul.d extend uphill and two down-hi11. It ia
a{vtsable for the instrumentman to carry al.ong ahand 1evel to
determine the approximate height at which theinstrument should be
set up in order that points to besighted wilt fall within the
established Iine of sight.L{r-z. LBVELING THB If,STBUIIBf,T.A
considerable amount of practice in leveling the, instru-ment will
be needed by a begi4ner. It is oniy by constantPractice that one
would really be able to feel and ex-perience the proper turning of
leveling screws to bring tliebubble in a level viar to its center.
Most conventlonallevels are designed uith fo_ur leveling screws.
The screwsare used to center the bubble in a leve1 tube which
isattached to the telescope of the instr.ument. Newer
modelsoften
-
have only three reveling screws to center the bubbleof either a
level tube or a circular bullrs-eye level. T,heprocedures followed
in leveling each type of instrument areoutlined as follows:1.
Instrurents Uith Four Leveling Screus. The bubble isfirst centered
approximately over one pair of opposlte Ie-
veling screws (Fig. l4-1). Time is wasted by exact cente-IAA
tEatuactgtT oFr r-.w- yEattctl otttatcat
rlng ln the flrst attempt, slnce the bubble wllL be thrownoff
during cross leveling. The telescope is next turned 90degrees
(either clockwise or counterclockwise) and posi-tioned over the two
other opposite leveling screws. Thebubble ls agaln centered
approximately. This procedure isrepeated about three or more times
with lncreasing careuntil the bubble finally remains centered in
any directionthe telescope is pointed. The instrument is leveled if
thebubble thus remain centered. This condition wi.Il occur onlyvlth
a properly adjuste! level vial since its vertical axisassumes a
truly vertical position when the bubble is cen-tered
+- oitaclim ot Subbla ltlovanrnt
trlotion of \L.tt Thmb
fig. l1-l . Cctttt itq hthb|2 ttith (ou.n leveLi.4g
lcr.clvll.
The thumb and the index finger of each hand are used toturn the
screws. Screws are turned always in opposite di-rectionsl that ts,
the thumbs should move either away fromeach other or toward each
other. It is only during finalcentering when just one screw needs
to be turned to movethe bubble thru a small graduation on the
level' vial. Itul11 be important to remenber that when the leveling
screwsare turned, the bubble moves in the direction of motion ofthe
teft thunb. Since all screws have exactly the samethread length,
one should be extended and the other Ehor-tened by turning in
opposite dlrectlons. Turning oppositeccrews should be at the same
time and also at about theaame rate. This procedure wlll altow the
screws to cons-tantly bear evenly on the foot pl.ate while the
instrumentts being leveled. The instrumentman must see to it that
theacrews.should be snug and not set too tight to avoid damageto
threads and the base plate. It should yield easily to aturn when
held between the thumb and index finger.
2. Instrurents Uith Three Level.ing Screrr. For instru-ments
wlth only three leveling screws, the telescope isturned until. the
bubble tube is positioned parallel to thellne through any two of
the screws. The bubble is then cen-tered on the level vlal by
turning these tso screws in oP-poalte dlrectlons. As usual, the
thumb and the index finger
a%
ttttutrnl u I dOtaattcaL ctttAnctt a'-| |Ar
-
of each hanal are used to turn the screws. Also, the
bubblewillstillmovelnthedirectionofmotionoftheleftthumb
Thetelescopeisnextrotatedaboutthevertlcalaxlsof the instrom.it
so that the bubble tube is brought per-pendicular to a line
through.the two Fcrews turned earlier.igai.t, the bubble !s brought
carefully to center by meansof the third screw alone. inis Pro6ess
of leve.ling is il-lustrated in Fig. L4-2Dirrction ol Bubbl.
Lov.n.nl.+
"t)
Molion ot \Lrtl lhumb
Fig. t1-2. Certz itg txthb,' tiil tl*ce 2zveling tfte/y4b;
The instrument is leveled if the bubble remains ".rrt"r-ed on
the Level vial when the telescope is brought back
toitsfirstposition.Ifthebubbledoesnotremainwithinit. center
graduations, the process is repeated until iti"n"i"" in lne center
for. any position of the telescope'inir-r""tnoa ot repeated
Benteiing wilI only.work if the Ie-vel vial is in aaiustmeft.
snould it be out of adjustrnent'no amount of repeated centering
will workIn automatic and tilting livels, a three-screw head anda
circular bullrs-eye level are usually empLoyed' Frigr toir;;ii;;-,*
ii i" inpirtant thar the 1e9s of the. tripod arepo"itioii.d so that
leveling head is nearly horizonta.l , andirr*-u"uufe in the
circular level is brought as close to thecenter of the vial. tlith
the telescope in any convenientpiriti""l- t;; bull's-eye bubble is
centered in one direc-iion UV operatint two leielingtcrews. It is
then centeredin the other diiection by meins of the third screrd.
The1o""."" of centering the bubblei is done by alternately tur-ning
two screw"
"nd then the other one singly' The teles-
.opJ ao"= not hive to be turried to. any direction during
theprocess of leveling.1I-3. HOLDIHG THE LB\IBLING ROD'The leveling
rod is held on /a point by a rodman when
asightis.tobetaken.onit.Toobtainthecorrectdistanceti6rn the line of
sight to the point on which the rod 'is
,l5o- ;[irf![i'f],i,,
ooo oo
Fig. l1-t. Ito{litg thc tod. placed, lt ls extremely lmportant
thatthe rod be held plumb when the readingis nade. The
instrumentman checks therda by observing through the telescopeand
notlng lf it is held parallel tothe vertical cross hair. If the rod
isnot correctly plumbed, the instrument-rnan gives out a signdl to
plumb therod.. The accuracy of a leveling opera-tion is
significantly improved if therod is alvays held correctly, hnd
italso increases the speed with which theuork may be performed.
The rodman either stands beside therod or behind it. He should
face theinstrumentman and see to it that the'rod is held nearly at
right angles tothe line of sight. The vertical side ofa building, a
smokestack, or a flagpoleare convenient aids to the rodman
injudging if his rod is pl.umbed properlywhen a reading is taken on
it. The 'rodis llqhtly supported between the fin-gers of both hands
and is allowed tobalance on its own rdeight. The f ingersmust not
cover the face of the rod. Therodman should see to ,it that the
gra-duations are always clearly visible andnot obstructed.
In high precision surveys the leve-J.ing rods used are eguipped
with a rodleve1. AlthouEh thls device is notgenerally used in
ordinary }evelingwork, it is advisable to use one wheninexpe/lenced
rodmen are empl'o1ted. Arod level. is securely held against theback
of a rod"or it'rnay be permanentlyattached to it. It should not i,n
anywayobstruct the rod graduations.LI-I. TTf,If,G A ROD
RBADING.Before readings are taken on a rod, it'ls important to
first examine how thegraduatlons aEe indicated on it. The
metric rod ln Figute 1{-4 lE graduated in centimeters
andnumerals are indicated for every fUIl meter and decimeternark.
The single dot shown bel.ow each numeraL lndicatesthat readings
taken on it'are ln the l-m range. Since mostrods extend to
lengths'of either 3 or 4'meters, three orfour dots are used to
correspondingly identify.each meterand declmeter graduation.
Each blackened graduatlon and each space between gra-.r.tuaa.a,
e l4l
. taaftc.L ottiltctt
-
r v !J
-
-duation ls one centlmeter (0'01 n) hlgh' The fuII
metermarksareidentifiedontherodby]'argenumeralswhichareusuallypainted
in red' The decimeter marks are identifiedby snaller niicX"-painted
numerals'In Figuge 1'l-5' the read-'ings for six difflrent
positions qre glven as examples' ItyilL be notej-that r."ilngr to
tliousandths of a meter are""1insggd ' as in
'd ana t wnf cn ate 2'155 n and 2'235 trlrespect ive 1Y.
fig. la-l. t'od gtailta'tioru. Fig. t{-5. Lztdit o luelhq
r,od.
3 2.235 m
3 2.2oom
: 2.165 m
: 2. l3Om
: 2.O5Om
E 2.OOO m
once the instrument is set up and I'eveled' the fol'low-'ing
steps are performed in taking a rod reading:
l.PositionTheRod.Theleve.lingrodisheldbytherodman on the
designated point w!fuse elevation is to bedetermined. He staids
beside or behind the rod' faces ittoward the instrumentman, and
holds it as nearly pLumb aspossible. since directions and signals
emanate from theinstrumentma'n, the rodman should a,Iways foius his
attentlono"-nitn. : ]
2. Focus on The Rod. The instiumentman ains and focusesthe
telescope on the rod at the same tlme seeing to
it-thatthebubblecontinuestoremaininthecenteroftheleve].":ilf
.-H"-;-Xr, "r;-at tfrr vertic4l
hair to check if the rodis held Plumb.3. Read The Rod. If the
self-reading rod is used'- theinstrumentman observes directly from
the telescope and re-
t
lc.a aaatu2caEtT 0F, I J?- Ja-iti.t nt.rttcrt
tcatuuEvac e I F.?tJtltrc.. gt srtnca,
-
| e:!
Fig. la-6. Tfu lzveling 4od oa {{:e, fr,to.ttlh the
tzlz*ope..
VcrticolCrorc Hoir
cords the .reading indicated by the line of sight.'The read-lng
is shown by the apparent position of the horizontal'cross hair on
the rod. The view through the telescope isrlmilar to that shown ln
Figure 14-6. Ifhen using a ta'rgettrod, the proeess of reading is
identical except that thetarget is set (raised or lowered) so that
the horizontalcross hair bisects it while the bubble is in the
ceirter ofthe level via]. The instrumentman directs the setting
ofthe target but the rcicl is read by the rodman. It. istxtremely
important that a check is made on the centeringof the bubble before
and after readings are taken on therod.I'-5. DBTBR}iIIIIIIG
DIPFBRBXCB IN ELBVATIOII.Flgure I4-7 illustrates a typical set up
for determiningdlfference ln elevation between two points, A and B,
usingthe engineerrs level and leveling rod.The sequence of steps
involved are as follows:
1. The instrument is set up and leveled at aabout halfway
between A and B.
point2. Sight on the rod held, vertically at point A and
rccord the rod reading. fn the given illustration the rodreading
at A is 2.00 meters. This means that point A on theground is 2.00 m
below the horizontal plane of reference(or Iine of sight)
established by the level.
3. Rotate the telesFope carefully about the verticalrxls and
sight on a rod held vertically at B. Record theroo reading at B. To
avoid instrumental etrors only one rodahould be used during the
measurement. The illustrated rodraadlng at B is' 3.50 m which means
that point B on theground la 3.50 m below the same horizontal plane
of refe-
-
rence1. The difference ln elevatlon between polnts A and B
is determingd by noting the dlfference inr thetr. respecttverod
readings or, 3.5O - 2.00 = 1.50 rn. This value correi-ponds to the
vertical distance between the two lmaglnarylevel surfaces (assumed
to be horizontal lines) passlngthrough points A and B.
Fig: l1-7. Utttrtitrittg difle,rcnce it cltvatiot.
Slght ot A Sighr ot B
From the given illustration, it can easily be seen tbatpoint B
is lower in elevation than polnt A since its veE-tical distance
measured downward from the established 1lneof sight is greater
thaJr that take,n at point A. Also, lfthe elevation of point A is
known, the elevation of point Bmay be determined by subtracting the
computed dlfference inelevation frcm the elevation of A. The
procedure justdescribed where the enginirer's level and a leveling
rodrdere employed for measuring differences in elevation igcalled
direct or spirlt leveling.1'-6. LEXGTHS OF SIGHT.It is always best
to take sights at moderate lengths toattain speed and accuracy in
leveling work. Ho*ever, veryshort or extremeJ.y long sights should
be avoided. The mostsuitable sight lengths-wi11 depend upon the
required degreeof precision, the surface of the terrain, the type
of ins-trument used, and uPon the distance at which the rodrernains
readable to the instrumentman. Under ordinary con-ditions the
length of sight should not exceed about 90meters where elevations
to the nearegt 0.001 m are desired.Beyond this length it is
difficult to read the rodl accu-rately and
_the errors cause.d by curvature and refraction,-
^ tattuaEtEnf 0F
, I T- vinttcat otsrttcct
r.
f-^oo
have to be constdered.Irregular refraction during sutnmer months
usually
causes rrbollingrr of the air. In such a condition,
therefraction is quite large and precise results could not
beexpected when very long sights.are taken. They should benade
considerably shorter especially lf the Iine of sightclears the
ground surface by only as much as one-ha1f me-ter. Extra long
sights, however, may be taken where theterraln ls fairly level,
only an ordlnary degree of accu-racy is required, and. completion
time is of 'primary irnpor-tance. Very short sights cannot be
avoided when the groundgurface rises or fa}Is rapidly such as in
mountainous areasand where the terrain is significantly rough.1'-?.
UAVIf,G THA ROD.By aligning the rod with the Vcrttcal cross hair,
the ins-trumentrnan can determine if a rod is held in a
verticalplane pas.sing through the instrument. 'He cannot,
however,telI if the rod is tipped forward or backward in thisplane.
This can.only be accomplished by waving th rod. Theprocedure is
used to determine whether.the rod is plumbwhen a reading ig taken
on it. It is accomplished by slowlyuavi.ng or tilting the top of
the rod through an arc, firsttoward the'inetrument and then away
from It (Fig. l4-g). TOthe instrumentman, it wiII appear that
the.cross hair ismoving up and down the rod.
.*
Fig. l1-5. &'ving t\e a.od.
As the rod is waved, the instrumentman takes note ofthe rod
readings which wirl alternatery increase anddecrease. The minimum
reading observed is considered as thecorrect rod reading at the
particular point sighted.when the long rod is used it is irr.y"
idvisable to
wave the rod. rf the target rod is used, it must be raisedor
lowered untiL there is found just one position when thetarget rises
as high as the rine of sight wrrir. the rod isbeing waved.1I-8.
CTNRYING THB INSTRUIIBXT.IThe level should always be h,qgt tn a
lbox when it is not
'-'oi!?"f'11*Rod Tilled--*\Forwcrd \\
,, ifJiii';,'!il't' El.iO
-
15-1. sOURCBS OF ERROR IN LEI|ELIIIG.The accuracy of leveling
work rnay be gffected by numerousfactors. However, it is not
difficult to obtain accurateand preCise measurements in levgling
aii theie.are differentsafeguards which could be taken agdinst
expected erfors andmistakes. Accuracy in leveling operations is
primarilyinfluenced by the type of instrument used. A great
dealwill also depend on the skills of the members of a levelparty
and the degree of refinement with which the wholeoperation is
performed. If correct leveling procedures andcare are adapted in
leveling work, systematic errors couldbe significantly reduced or
eliminated. The remainingerrors expected to oicur would onty then
be random errors'
The principal sources of error in leveling work nayemanate from
either instrumental, personal, or naturalerrors. These sources of
error are each discussed be10w asto their nature, .magnituder and
how they may be minimizedor eliminated.
,1. lnstruental Errors. These errors are attributed toimper f
ect ions in the instruments e ither f rom :fcul'ts inthelr
manufacture or from improper adjustment. In levellngwork
instrumental errorb ire usually dqq to a defectivetripod, a
levellng rod not of standard length, or when theinstrument used is
out of adjustment.
a) In*truEnt ''Orat ,.of Adjustrent. Tbe most
commoninstrumerital error is caused by the level being out of
ad-justment. Particularly significant is when the line ofsight of
the telescope is hot parallel to-!h. axis of thelevd1 vial. The
line of sight witl be inclined either up-ward or downward when the
bubble is brought to the centerof the tube. lfhen a reading is
taken on a rod, the resultis an error consistently either plus or
minus, and with amagnitude which is proportional to the distance
between theinstrument and the rod. This source of error can be
elima-nated or kept at a minimum by frequently testing'the
ins-trument and keeping it always in good adjustment. The
errotwitl. also be greatly minimized or eliminated if the
back-sisht and foresight distances are kept nearly equal. Sinceit
would be difficult to predict when an instrument goesout of
adjustment, thF latte'r method is the mo,re certainand should
always be used for careful .Ieveling.
b) Ro4: Not Standatd Lengttr. It is possible to haveinaccurate
graduations or divisions on a rod. This isusually due !o
imperfections in their manufacture. In'accu-rate rod graduations
can cause errors in measured verticaldistances similar to those
resulting from incorrect mar-kings on a tape. In any case, a rod
of, incorrect lengthwill introduce a systematic error in lev-e1ing
work
It is important that rod lengtfrs dYe compared perlodi-cally
with a standardized steel tape. Any error in length
trQ9- i f | | i{f"" f i!, ! i " " "
ahould be determlned and necessary correctlons applled totII
measurements nade wlth the rod. ALso, the rod must al-UayB be
handled carefully. A Philadelphia rod is easilydamaged when the
upper part of the rod is alloued to stiaedovn so rapidly that the
blocks on the two sections areerushed. Its bottom should be kept
clean when used in muddytreas or where the ground is relatlvely
sof,t. If the rodmanla not careful, he nay easily have some amount
of soil,clay, dirt or mud sticking to the bottom of the rod.
Thisgln cause severe errors in leveling.
c) Dcfoctlve ?rtgod. tne movement of the ievel dueIto Eettling
of the tripod legs can cause possible errors inilcvel!,ng work. lhe
trlpod usuaLly settleE in soft ground ordue to vibrations caused by
passinE ve'hicular traffic. Itimportant to always set up the tripod
r,igidly as this
n lead to erroneous measurements and waste of time. Boltstnd
nutstat hinged joints of the tripod should be checkedle.gularly and
tightened. To avoid sliding of tripod legsdue to vibrations, the
instrument should be set up oply attlrn and stable. ground. Smooth
surfaces such as concretepavements and steel plates should be
avoided.
2. $$tlobal Brrors. Although personal errors occurlargely' du
to' the llmitattons of the sences of toueh,rlght, or hbaring of
individuals, the aki1Is, training, and'tearnvork of ,the members of
a leveling party are also majorlactors to be considered. Personal
errors are usuallycaused by er'roneous manipulations'and careless
handling of
' tnstruments when making observations. Such errors includethe
foll.owing:al Ertrblc 'No-t Cairtered. Rod readings will be in
crror when the bubble is not centered in the level viaI.lhe
magnitude of the error depends on how sensibive thevial has bebn
designed. Thefe are various conditions in thefieLd which nny cause
the bubble not to remain centered. Itcould be caused by a tripod
leg settling in soft ground,the instrument may not be level.ed
properly or it may be outof adjustment. These are factors which
could all be attri-buted to carelessness on the part of the
instrumentman.
the instrument should not be handled unnecessarilyafter it is
set up and leveled. Its tripod should not begrasped when taking a
sight, and vertical pressure exertedon any part of the instrument
shor.lld be avoided. The.errorintroduced by a bubble which is not
centered varies as thedistance fron instrument to the rod. It is
therefore impor-tant to exercise great care in leveling the
instrument whenextra long sights are taken
.' b)-Parillax. If a pressure gauge or any graduatedcircular
meter is viewed from different angles, one willnotice that. a
number of sliqhtly divergent values could beread. This is due to
the effect of parallax. Howeve!, ifthe pointir and scale of the
gauge nere posit-ioned at
tEasuac.ttrof l4.lvEnrtcaL CtSrttcES E I v-.!l
-
exactly the same plane, parallax woulQ be totally ellmlna-ted. A
similar condltlon occurs when sightlng through thetelescope to read
a'levelIng rod. The effect of parallax lato cause relative
displacirnent betieen the frnage of thecross hairs and the inage
formed by the focuslng lens. Pa-iallax cbn be elimlnated by careful
focuslng of the teles-"cope untll no apparerit movement of the
horizontal hair re-Lative.to the rod can be detected when the eye
ls moved up,and down while sightlng, c) Fral,til 1fi{d,.t*rilin{tl.
The instrumentrnan at times
nay misread the number of meters,and decimals when taklng arod
reading. An-incorrect rod reading is'usually the resultof the
hngth"of cight', po(lr ueather condltions, and theskill of the
lnstrumentman and the rodrnan. In ordinary Ie-veling work it is
advisable that the length of sight shouldnot exceed 90 meters. The
number of reading errors iEslrgnificantly reduced when short sights
are taken. Uhenlong sights could not be avolded, a series of
readingsshould be taken on the distant rod and only the mean
rea-ding..should be used. Extra long sights are common such aswhen.
levellng across a wide rtver or a deep ravine.
In precise leveling work, instruments used are equippedwith
three horizontal hairs. Threi readings are usuallyrecorded at each
sighting. Since the two extra halrs (orstadia halrs ) are equally
spaced from the center rqlddlelralr, the dif ferenc'e between the
readings of the middle andlower halr should be equal to the
dlfference between thereadings' of the. middle and upper hair. The
instrumentnanshould take ttm-,-to compare these two quantities
beforetransferring to another set up sinbe it is an
effectiveprecaution against faulty rod readings.
dl li$"f,ot llild Plurb,. Aslde froJn holding the rod ona flrm
and definite polnt, lt should also be held as nearlyvef,tical as
possible. If it is held off the verticaf itslll be intersected by
the line of sight farther from the.bage and the reading will be
much greater than what itshould reall.y be. The reading on the rod
sill be lowestwhen it is held plunb
Appreciable lncllnatlons of the rod should be
avoidedparticularly when a hlgh rod is used. In differential
leve-ling, er.rors due to non'verticality of the rod tend to
com-pensate at turning polnts, however, if the foresight read-tngs
are consistently greater than the backsights, theerror becomes
cumulative. It is easy to determine if therod is held pl.umb or not
since it can be checked if it isheld parallel to the vertical cross
hair. However, the ins-,trumentman cannot check lf the rod is
leaning toward oraway from the instrument. Thls type of error'can
be avoidedlelther by waving the rod or attaching a rod level. to it
tofacllitate holding it plumb. The use of a rod level allowsthe
rodman to plumb the rod,by sinply centering the bubble.Its use is
preferable to swinging or waving the rod
e) Irecrcet 8:ttlng OI lergict. It is important to)C.,
tEputEattr oF
rllir- vEattct otsfatcEt
I
always handle the lcvellng rod,carefully. The rodnan attlmes
fails to set properly the target when a high rod rea-dlng ls rnade
wlth lt. During use, the target nay slip down-uard because it is
not clamped firmly at the exact positionslgnated by.thr
instrumentman. To avoid this type of error,the lnstrumentman
sh"oulil always take a second sight on thetarget after 'it
is"clamped by the rodman in order to besure that it has not
slipped
f ) ,Unrqprl lac}llght and Porcslght Dlatalrcs*i Inleveling
rrork it is usually good practice to make backsightand
corresponding foresight distances nearly equaI. In sucha practice,
errors due to imperfect adjustment of the ins-trument and also
those due to curvature and refraction arereduced or totally
elimlnated s.ince the error " in the bach-sight is equal to'that in
the foresight.
It ls sufficient to approximate only by eye foresightand
backsight distances in ordinary leveling work. For moreprecise
uork, pacing, direct taping, or stadia measurementsare employed in
determining sight distances. Balancingforesight and backsight
distances, however, nay not alwaysbe practical or possible. Thls
situatio.n may occur when theterrain is extremely rugged or when
Leveling across widerlvers. For example, in levellng up a steep
slope the dis-tance to the foresight wlll be about one-half the
distanceto the backsight. The two distances could still be
heptnearly equal by properly posltioning the level a
certalndlstance from the straight Iine between the turninE
points.The whole length of the level.route is traversed by a
zLg-zagging nanner in order to eliminate this source of error.
3. Irtural Erzors. These are errors which are due tonatural
sources and could not be totally removed but theireffects can be
reduced by applying corrections and usinggood judgment. Such
'errors include the effects of theJarthts curvature', atmospheric
reqraction, variations intemperature, wind, and etc
a) &rveturc of thc lrrth. The ef fect of curvatureof the
earth is to lncreaSe the rod reading. From thissource the error
afiounts to .about 0.0? cm per J'00 meters.This error is introduced
even tf the instrument used is inperfect adjustment. It, however,
only occurs in extra longsights and when backsight and foresight
distances are notmade equal. Since sight distaneeE in ordinary
leveling do'not vary significantly, the resul.tant error arising
fromthis. source is so small and ls considered a,
negligiblen""";i:I'rong
sights courd not be avoided, the error may beellminated
.
by appLying a correctlon to the computed diffe-rence in
elevation or by employing the method of reciprocalIeveling. In
other situations, the error due to curvaturecan be eliminated
by'keepin{ the backsight and foreslghtdlstances from the same set
up nearly equal.
* i,',21!'i!!171"1tr
-
I -6!,
-
b) AibfDrpherlc lgfractlon. The pregence of heatwaves on a hot
day is a sign of rapldly fluctuating refrac-tlon in the atmosphere.
Reading drrors are Iike1y to occurwhen heat waves are present since
it makes the rod appearunsteady when a sight iE taken on it.
Sincqthe refractionls usually larger when sights are taken close to
the groundsurface, the line of sight shoul,d be established at
leastone meter above the ground. Because it may be impossible
toread the rod when heat uaves are particularly intense,leveling
work" should only be resumed when heat waves sub-side.
To reduce the effects of atmospheric refraction onlyshort sights
should be taken. Balancing the lengths ofbacksights and
foresights.aLso elirninates errors due torefraction. Its effect is
negligible in ordinary leveling,but in precise leveling, combined
corrections for curvatureand refraction are applied to observed rod
readings.
cl Tcqrerature Variatlons. Changes in temperaturecauses leveling
rods to either expand or contract and thesecould introduce errors
uhen taking rod readings. To guardagainst such effects, invar or
nllvar gr'aduated strips areused on rods for precise leveling work.
Heat also cauEes
.w4rping or twistlng of the parts of a level. The liquid inthe
level, vial expands and the bubble shortens when it isheattid. This
temporar'ily disturbs the adjustment of theinEtrument and may
affect the accuracy of rod readings. It
. is prefetable to use a surveying umbrella since this
willprevent the rays of the sun from falling directly on theLevel
and thus reduce the effects of heat.dl,flnal. A strong wind can
shake a leveling instru-ment making it d,ifficult to center the
bubble in the levelvlal,. It can also exert a suf f icient amount
of force tocause an extended rod to vibrate making it stand
unsteadyand hard to read or plurnb. If leveling has to be
perforroedduring windy days, the instrumentman should either
exertefforts to shelter the instrument or wait for a tull in
thewirrd. Setting up the level behind a building or close to alarge
tree trunk shouLd reduce the effects of wind. In an'open field,
long sights should be avoided to limit the useof a high rod.
e) StttlGDnt.of the Inrtrum{rt. In soft or thawlngground, mudr
Bnd swamps the instrument may settle in thelnterval of .time
betfeen rod readings. This source of errorris cqmulative since
every settLement of the instrument in-creases the computed
elevations of all other observedpolnts by the amount of the
spttlement. Errors due to set-tlement can be avoided if the
instrumentman takes thenecessary precautions to insure that the
level is alwaysset up on firm and stable ground. It is also
important thatas ]ittle time as possible should be taken between
rodreadingsi
.rtrrav Turnrng pornts. rn differential revelingwork, a poorly
chosen turning point may be a source ofIAA tEAtutcuEtr oF
error. Thls condttion is slmlrar to that resulting
'fromsettlement of the lnstrument. rt is a cumulative type oferlor.
since two rod readings are arways taken at a Lurningpoint from
different set ups of the revel, it is importanito select firm*and
sbrid turning points. They must also beeasily identified. care
should be taken not to strike therod against the turning point or
to exert any.pressure onit. rn soft and unstable ground, it is
adviiable to use apeg or a steel plate as a suppor,t to prevent
settrement ota turnlng point. The. instrumentman shourd guard
againstmovement of the turning point and the rod should be h;ld
atexactly the same point when another reading is to be takenon
it
\5-2. @xl{oN l{rsTtKEs Ir{ LByBLrtrc.The folrowing are some of
the most comrnonry nbde mistakesint leveling work:
1. l{isreading The Rod. During leveling the instrument-nan may
occaFionally read the rod incorrectly; for example,he nay read 2.?5
m instead of 1.?5 m. This mistake mostfreguently occurs when the
line of sight to the rod is par-tially obstructed by vegetation or
other objects in thefield. It is lmportant that the instrumentman
always care-fully note the fu1l meter marks above and below the
ob-serve rod reading. Also, it is preferable to call out read-lngs
as they are taken or to use a target, and lie-re the ins-trumentman
and the rgdnan take and compare their respectiveread ings
2. Incorrect Recording. The pecorder should always callout the
readings as he records them in order to prevent therecording of
incorrect varuesl, To detect mistakes in recor-ding rod readings,
the best method is to read the rod,record the reading, ,and
then