Surveying

Co tentsIntroductionBasic principlesPlane Table SurveyingChain SurveyinglevellingTables

page13811'933

PIN

EQUIPMENT

BOAT LEVEL

ALlDADE

o

TRIPOD

PLUMB BOB Fig 1

PLANE TABLE SURVEYRADIATION METHOD

Factory

------

,,\

MARTINS LANE

A PLAN OF A TYPICAL SITE

Fig 2ID

CHAIN SURVEYING

Chain Surveying has long been established as the easiestan basic form of land mea$urement and is still in common use.3ased on triangulation and consisting of carrying out thesurvey in the field and plotting the survey to scale in thedrawing office from recorded measurements in the field book.~t is a job for two people the surveyor and his assistant.

There are several possible inaccuracies which may occur'.'hencarrying out a chain survey and great care should be~aken to avoid the,. The most common being confusing the-~llies, miscounting the links, the chain having knots in

ink joints, bent links, the chain not being laid out in astraight line between stations, incorrect bookings, miscalled·i ensions and booking offsets at wrong points. Practice in~he field will highlight some of these problems as there is~o substitute for experience in the use of a chain.

EQUIPMENTThe basic equipment for chain surveying is the metric

chain 20metres in length with 100 links each .20metres in_e. th. Every tenth link is marked by a brass tag or teller'-it:-tintermediate tags for every link. The chain is made ofE eel wire and great care should be taken when folding so as~o avoid entanglement and bending the links. When the chainis to be used and laid out it is done by grasping both:a~dles of the chain and throwing it out in one operation and~ .en straightened out ensuring all links and joints areoutst ret ched properly.

There are two other chains used these being the GunterChain which is 66 feet in total length with 100 links of7.92 inches, and the Engineers Chain 100 feet in length and:.~E_00 links each a foot long and marked at 10 footi:r:tervalsv:ith tallies accord.ingLy ,

TapesThese are made of steel being the most accurate and being

r-e I'er-r-e d to linen tapes. They are cornmon.l y in lengths of 10,20 and 30 metres and are used to measure offsets to the mainchci.nline.

11

EQUIPMENT

90

THE METRIC CHAIN

TAPECHAIN ARROWS

"g 3

((RANGING POLES

POLE SUPPORT /.,. e'

12

ArmlWS

.-.•. 0 ':c are used to mark the end of each chain line and areJOOmm to 450rmTlin length and carr-y a red cloth

so that they can be easily spotted on the ground.

poles:~ese ere usually 2 metres in length of wood or metal

. :n bands alternately in red, white and black.

book:::"e_d oak approximately 100mm x 200mm with entries

at the back continuing to the front so that the_ ._:~~c are recorded in the same direction as the Surveyor

c.::'-:':::F' along the chain.-C~~~::.~C.re entered in the book such as hedge"', fence8,

~~~ coundaries, buildings, trees, manholes and polesetc.e afore mentioned are illustrated in Fig.J.

orocedure iE to make a reconnaisance of the sitethe f,ener~l shape and layout and any other

o be surveyed. Then decide on the framework of-.::.----a ion and drive in station pegs A. B. C. as shown in. . :~€stations to be fixed by taking two tic lines to

: ~o that it can be re-located if a return visit isC"~:.~S> If the distance between the stations exceed a

::'e:::-thline in with an intermediate ranging pole as·f.5. Then by p~oceeding up the chain line from.easure with 90 offsets, features as beforeu~til you have reached the end of the line A-B,

• ::. - ";;0" n all the relevant information. This is then-E' ~or B-C and C-A. If the 900 offsets exceed 9 metres

-~~.t en an Optical square can be used to give greaterr.=-'''''-:'_'''''''~:' or the J:4:5 Triangle rule employed using a tape.

ractical nature of the survey has been carried- ~r_e::ullv checking that all the information required has

. ':"noted and loeged the Eurvey can be drawn to scale:!f:..'.'.in[; office.

13

RECONNAISSANCE & SETTING OUT STATIONS

The S· e_.ClllJjAP ,.(~~. _

Fig 4

14

CHAIN SURVEYING

intermediate rangingpole

SETTING UP CHAIN LINE Fig 5

15

CLINOMETER

_~s ~ strument is used for measuring slopes of 3' oris simply illustrated below. By firstly viewing~nstrument on the horizontal plane the instrument

and focussed onto the ranging pole up theope with the counterweight in the vertical position

- ~ ~_evation can be read on the dial, in this case 300•- strument is hand held and is most useful for

slopes quickly and easily giving instant readings

16

CHAIN SURVEY

SLOPING SITES

To measure "Leg" slopes greater thano3 , measure convenient horizontaldistances, plumb down to ground levelto fix point from which to take nextmeasurement.

B A

~e of slope with CLIlWJ·::ETER''0(11Trigonometry AB=AC Cose{.

measure slope

------

- ------ --->--....---- ---- --- --- RANGING OVER HILLS-----CLES

c --- - --

ft and B. AssiEtant ~ith pole 2t D lines in surveyor"t C on line AD. Surveyor linef'in pole at D on line

sequence ~ith four poles in line.

17

b d e

B E

cain line through A.B.C. set out equal offsets to a.b.c.i~ d.e.Set offsets of length as before to fix D & E.~~ continuation of main line through F.G. etc.

'~------~------~------~------~D

1Il:dll"\IIWl G ACROSS A RIVER

-----__ ~_------=rtIVER -

:es at A & B on chain line. AD at Rt. 1s to AB. Pole C-!: na t AC=CD. DE at Rt. 1s to AD, wi th E.C.B. on straight

::"enAB =DE.

EY OF LAKE OR WOOD

- - ~ fraJework of chain lines_= area and triangulate

- _ -ies across the corners_:'e'; C:- IN TRAVERSING.

18

I TRODUCTIONThis book has been set out to illustrate the fundamental

basis of land measurement and procedures to adopt whensurveying areas of land. The actual practice of carryingout surveys has not changed much over the years with onlyperhaps the refinement and advanced equipment now in use.Wost of the procedures detailed in this publication are incorr~on practice and will give a good grounding toArchitectural, Surveying and Building students.

It is emphasised t.at only practice in the field willgive a good and thorough understandinG of the methodsoutlined here and the key being accuracy in performance.

1

LEVELLING

___ ~asic instrument for levelling is the surveyors.••-:;,_<::;;:;.=- __e '!hichis an adaption of Keplers telescope ernp loyang

-__-ex Lenses which produce a real image and line of_ line of collimation (i.e. principal axis) and will

-seus sed in more detail later. The other piece of_~-~~- used in conjunction with the level is the

_ ~~-_~c _evelling stave in 4 metre and 5 metre heights.-~ :s are taken using the sight line throueh the telescope-_ '= ::"e'.-elonto the staff wlri ch is collimated in metres and

Readings of course will be inverted, this will beater.

_.::!: =o::"_o'tingstatements are accurate for most practical

=_:::'onof transparent material bounded by either planee:'surfaces.

_:==ere~t types in use: (Fig.l.)

{fJR/A./CIA9L IlxIsOr al..5.

Fig 1fJL!J,UO COA./c4V£

right angles to the two parallel tangentc: of theurfaces of the lens.

reon the principal axis whose distance from the tRO

_ :'sproportional to their radii.

19

- -~~c~~ fro. one transparent material to another- -~~ec~ion. For example, a stick partly immersed in-_ears to be sharply bent at the surface of the water

r-or above the water surface. Thus, in passing:e~s the rays of light will be bent or refracted ase -. ';;ith a convex lens the rays of light will~ _assing ttrough it.co__ea e lens the rays will diverge on passing through

lens is suitable as a burning glass while

through a convex lens will converge on ahe principal axis called the "principal focus"

- ::'~:::". The distance from this point to the optical-::e :ens is termed the "focal length" of the lens.

Fig2ib.IS,

~ c ~ ex lens ~ill produce an image on a screenT_is imat;eis termed a "Real Image".

ens however causes the light rays to divergepr-oduced backwards to the principal focus.

i".c.gev:ill be seen on a screen at "F" and this is',-irtualImage".

len th of a convex lens is positive (+)length of a concave lens is negative (-)ion of different shaped lenses will produce a

~ocal length related to their individual focal-_,eexpressionI

+ + + •••••••••••

:-C~_ length of the combincation, or, compound lens,- ~!" " ov:nas the "jiowe r" of the lens.

I etc.fJ'

the focal length of individuallenses.

20

Production of an imageAn object being viewed through a lens is considered to

consist of a number of connected points, each radiating tV10rays of light; one ray passing through the optical centre ofthe lens without being refracted, the other, parallel to theprincipal axis, refracted through the focal point, bothintersecting to produce an inverted "real image" (See Fig.3.)

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focal length fU for a lens.

There is a definite relationship between theand the object distance V to the image distance

This is expressed as:I I If = + 11V

andI 1 If = V U

for a convex lens.

for a concave lens (where f isnegative)

As the image must be produced on the same plane as the crOLShairs of the telescope of surveying instruments, and thedistance from object to lens will vary causing a proportionalvariation in value U, it is essential to provide adjustment ofthe lens by a focussing mechanism.

A single lens hov:ever possesses a number of faults, the twoi portant ones being:

(a) Chromatic aberration; v!hite light is split into itsco ponent colours on refraction, terr-:ed"dispersion",and due to differing angles of refraction for eachcolour the image tends to be blurred and surrounded bya halo of colours.This is usually overcome by using two lenses ofdifferent material, e.g. one of crown glass and one offlint glass.

(b) Snherical berrationj Thic is caused by various rays ofliGht fIling on the lens not beine; r-e f'r-ac t ed to passexact Ly t hr-ough the SC:.T:iefocal point. ~'l)is f'auIt iscontrolled by using thin Leris es and restrictine; theobject to be viewed to an area close to the princip~laxis of a flc:..tcurvature lens.

21

The telescopeThe surveyors telescope show~ in Fig.4. provides a line of

collimation passing through the optical centres of the lensesand the cross hairs. The e epiece magnifies both the realimage and the cross hairs in the same proportion as these areboth on a common plane. The eyepiece is usually the Ramsdentype, consisting of two pIano-convex le~ses mounted a shortdistance apart in a self-contained case, wh i ch is threaded onthe outside to allow it to be screwed f'orwar-d or back in thetelescope body to bring the cross hairs and image into clearfocus. This arrangement of lenses reduces spherical aberration.The object glass is usually a compound lens to reducechromatic aberration.

Focussing)

/MIlCr~ Fo.(?N/£DBY #£' PIECt.

I'12/AJC /P4L.. 4;<15.j.!1../£ e>,r COLJ.IMI17IoA/1..11./&o.t: SI(jIlr:

Fig 4Two forms of focussing mechanism are used to bring the

image onto the cross-hair plane as the distance of the objectfrom the telescope varies. These are:

(a) External focussing: The body of the telescope is madeof two concentric close fittinG barrels, the objectglass mounted in one and the eyepiece and cross-hairsin the other. A rack and pinion mechanism operated bythe "focussing screw" advances or retracts one tube inrelation to the other, thus increasing or reducing thedistance between object glass and eyepiece/cross-hairs.This method was common on older instruments and is moreaccurate for tacheometry purposes, but has thedisadvantage that wear on the tubes may allow entry ofwater, dust, etc., and impair the efficiency of theinstrument.

Cb) Internal focussing: A double concave lens mounted on ()frame is fitted inside a one piece telescope bodybetween the object and eyepiece lenses. The framepocition is adjustable by means of a rack and pinion,as before, which slides the lens tov:ards or away fromthe object glass.

22

The concave len disperses the light rays from theobject glass to greater or lesser degree depending onthe position of the lens and thus allows focussing ofthe image on the cross-hairs. The disadvantage of thismethod is the loss of brilliance due to the extra lens.

Cross-hairsOriginally, spiders yeb was used, but these broke easily

and were difficult to replace. Today, very fine lines areetched on a piece of very thin optical glass fastened to a"reticule", forming an interchangeable capsule which fitsinto a flanged metal ring called the "diaphragm", held in thetelescope barrel by four capstan headed screws - which shouldonly be touched when changing or making major adjustments tothe cross-hairs.Parallax

This term refers to relative motion between the object andthe cross-hairs when the eye is moved to and fro across theeyepiece, and means that the image and cross-hairs are not onthe same plane. To eliminate parallax a piece of white paperis held in front of the object lens and theeye-piece moved inor out until the cross-hairs stand out clear and black. Thetelescope is then focussed on the object and tested forparallax again, the procedure being repeated if necessaryuntil the parallax is eliminated.The spirit level

Cormnonly fastened to the ba.r-r-e I of the telescope on alevellirig instrument, but usually on the top plate of aTheodolite. The more sensitive spirit-levels are barrelshaped curved glass tubes, with the less sensitive only aportion of the surface is curved, when thee'termed non-reversible levels. The glass tube is filled with ether oralcohol with a sm2.11air space left to form a bubble. Thesefluids are less viscous than water, ~nd have a much lowerfreezing point, but a greater ey-pansion, so that a level leftin very hot sun may burst.

The top surface of the tube has graduations etched on itwhich aid in centralising the bubble in the centre of its run.

The sensitiveness of the bubble is defined as the amount thehorizontal axis of the tube has to be tilted to cause the bubbleto move from one graduation mark to the next, e.g. 1 division)0 sec. means a tilt of )0 sec. of arc above the horizontalv.Ll L cause a "run" of one graduation.

23

The spirit level tu e is e~c osed in a metal case,attached to the body of ne L_ trur.!entby one or two capstanheaded screws which alLov the tube to be adjusted so that itloneitudinal axis is paralle to the principal axis of theTelescope.

By this means one can adjust the instrument so that theline of collimation is horizontal, i.e. at right a~gles to theplane of gravity acting at the centre of the instrument: Donot adjust the capstan screws unless making a majorcorrection.

The centralising of the bubble may be observed in differentways. On some instruments the tube is viewed in a rnirrorhinged to an angle of about 450• In other cases an internalmirror may be used, or a right angle prism, to give thesurveyor an image of the bubble in the eyepiece so that hedoes no~ have to move round the instrument.

Another method presents two half bubbles images in thefield of view and these have to coincide to form one completebubble to bring the telescope level.

The circular or "cats eye" bubble is inferior in accuracyto the level tube but gives an approximate level plane forinitial "C'uickset" levelling purposes.

Types of levelsDU.DV Level: The simplest form of level consists of abubble tube attached to a telescope which is rigidly fixedto a horizontally rotating centre post and top plate, in itsturn connected to a bottom plate by three or four levellingfoot screws, which can be adjusted to bring the spiritlev~l and telescope axis horizontal.

T~o conditions are essential for accurate work.

1. The axis of the bubble tube must be parallel to theaxis of the telescope, i.e. line of collimation.

2. Both must be at right angles to vertical axis of theinstru ent.

Tilting Level or Quickset Level: An improvement on theDumpy as the telescope can be pivoted in the verticalplane by means of the tilting screw under the eyepiece endof the telescope. It is only necessary to set theinstrument to an approximate horizontal plane byreference to the "cats eye" bubble, the telescope beingbrought level for each sighting by using the tilting scre~.

)

example

24

Precise Level: This is a development of the now almostobsolete Wye level and the Tilting level.The telescope tube may be tilted and also revolved in itsmountings so that b taking the mean of two readings onthe same station a true reading may be obtained, thiscompensating for any error in the collimation of theinstrument.

example

Terms used in levellingBench rark: A fixed point on the earth's surface whose

level above Ordnance datum is known.

Ordnance dat un.e r~ean sea level to which all other levelsand bench marks are related.

Back sight: The first sight taken from a given levelposition.

Foresight: The last sight taken from a given level position.

Intermediate sight: Any other sight taken from this levelposition.

HeiGht of Instrument: (H. of I). The height of the line ofcollimation above the datum. (i.e.si ht line or principal axis oftelescope.)

25

Reduced level: (R. =.. Calculated height or level of apoin a 0 e or below the datum.

Change Point: The point at wlri c h both a foresight andthen a backsight are taken (i.e. when thelevel changes position.)

METHOD

Setting up the level1. Open tripod legs to 600 and press the feet firmly into

ground.

2. Note how instrument is packed in the box beforeremoving and lift out carefully, never by thetelescope tube.

3. Screw firmly onto tripod head; never crossing thethreads.

4. Roughly level the instrument y adjusting the tripodlegs, complete adjustment by means of the footscrews,i.e. bring the bubble to the centre of its run.

plan

c:;~. axis at ric;ht ofent:

Check that there is no play on the axis of theinstrument. Turn telescope over a p~ir of footscrewsoand level-up. Then rev rse tube through 180 • If thebubble runs off centre bring it halfway back withfootscreVls and the balance of the way with the capstanhe ded screws on the bubble tube.

26

CorrectionsCurvature: as the eart.h is curved, a horizontal sight

does not give the true relati e heights of two points overa long sighting distance. See Fig.6.

.As C is so small cor.:paredto 2R it is ignored and theexpression is written thus X2

2R = correction.

Distance 2 d2i.e. curvature correction measured or

Diameter of Earth 2R

Refraction: differin~ atmospheric conditions cause therays of light entering the telescope to be refracted, i.e.bent, towards the earth's surface to greater or lesserdegree, so that on a long sight the reading seen on thestaff is not on a true horizontal line but below it andnearer to the earth's surface than it is believed to be.

This error due to refraction partly offsets the errordue to curvature. As an average figure it is assumed thatthe error due to refraction is 1/7 that of curvature and inthe opposite direction.

The combined correction for curvature2and refraction isusually quoted as a deduction of 6 d7 x 2R from.the staff

readlng.

R

Fig 6

27

For short sights t::&ci::ere:!1ceis so small t11Citit De.' beignored, but in exact Ieve:l~~ sights should not exceefi aquarter of a mile to a Ol ::"euncertainty caused by theseerrors. By taking back a.. fore-sights to staff positions atnearly equal distances fro _ t:he level these faults may beconsiciered cancelled and are not calculated in normallevelling operations.

o,,/1 /)/S7,tftJCc~ ~r 1~ (y ----f,--..1-J---./'{

Co J pound Levelling: in whi.ch the levels are obtained onlyby changing the position of the instrument as one follows theundulations of the ground in a long line of levels, or toobtain clear sights which <::.reotherwise obscured by obstacles.Therefore there will be:

Forms of levellingSimple Levelling: in which all levels are obtained with

the instrument in one position, or, in other words:

(a) there is onl T one line of collimation.

(b) the first sight is the only backsight.

(c) the last sight is the only Foresight.

(d) All other sights are intermediate sights.

E

220 1/5. . 2-Se ---/I'" '::":::"_-!F2~

B cI,-.,

(a) Kore than one line of colliDation.

2'/0

F

(b) A bo;;.cksie;l1tand foresight for each change in instrumentposition.

A I" -,J F_yl. ~~~---~.--------~r--~O~~/~~~~~--~~~l----~~----l~·_'( 1 1 '1 1

(c) Separate groups of intermediate sights reI ted todifferent instrument positions.

Fig 11-70.--------

.{)O2'00.

28

LAND SURVEYING

GENERALLYThe main function of carrying out a practical land

survey is to ascertain as accurately as possible the sizeand shape of building sites, fields or other areas of landmasses. They may have on them ponds, buildings or includeother features such as ditches, streams and trees etc. whichmay need to be recorded and plotted on a survey dravring.This is generally known as land measurement.

In addition to this information it will also beimportant to·know how the site slopes for which you willneed to carry out a level survey. Basically it is forminga three dimensional picture of a particular area of landwith points of elevation marked on it so that verticalcan be taken through showing planes of elevation.

There are various methods of gathering this informationwhich will be illustrated and explained in this book. Itwill be necessary to have knowledge of geometry and a goodunderstanding of mathematics in order to plot and calculateinformation gathered by the practical survey.

Experience and practical knowledge can only be gained byactually carrying out the methods and procedures describedin the field.

There are two basic methods of land measurement in buildingPlane Table Surveying and Chain Surveying, these will bediscussed and illustrated more fully in the following pagesof this book.

Other methods include the use of the Theodolite which isused for measuring horizontal and vertical angles. This isused mainl:y in Civil Engineering work i.e. roadconstruction etc. where greater land masses and distancesare involved.

Over larger areas of land the curvature of the earth'ssurface will have to be taken into account and is known asGeor'ieticSurveyine;. It is used in Ordnance Survey work andis a specialised branch of land survey work.

2

BOOKINGThere are two forms of booking down level readings,

Collimation also known as Height of Instrument and Rise andFall method.

Rise & Fall MethodUsing Fig.l. to illustrate this method the readings taken

by the level are entered into columns of either Rise or Falli.e. the reading A datum is entered into the back sightcolumn with reading B entered into the foresight column.As B is smaller than A this denotes a Rise and the differenceis entered into the Rise column and recorded as such with areduced level reading entered by adding to a datum figureof 100.00. for level at B.

Any intermediate Sights are entered into the appropriatecolumn with reduced levels accordingly. Distances andRemarks Columns are used to record change points and levelpoints etc. This method makes it possible to check each pageby adding the Rise column and Fall column, the differenceshould equal the difference between the backsight andforesight column as illustrated below.

RISE & FALL METHODSAC!:: jA/T[J:( rcRE- RISE /"JJLL RlIJ/la~ /JIS1~E RlMllRKSSI{H-IT srcrllT SJaI/T ,uy£L

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29

COLLIMATION METHOD

Collimation MethodAgain using Fig.l. to illustrate this method the

succeeding reading is subtracted from the last calculatedcollimation height i.e. reading at A is height of instrumentbeing 102.00 after datum of 100.00 is added. This will thengive a Reduced level at each staff position.

To check add the back sights and add the foresights andfind the difference. By finding the difference between thelevel of datum and the last reduced level should equal thedifference between the backsight and foresight totals.

Always check if possible back to the datum point bytaking flying levels this will avoid a return visit to thesite.

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30

SOURCES OF ERROR IN LEVELLING:

Incorrect setting-up of instrument.

1. Bubble off centre when taking reading.

2. Movement of staff from position when changing levelstation.

3. Staff not held vertically.

4. Parallax - adjust.

5. Instrument knocked or moved during backsight-foresightreading.

6. Staff not properly extended and locked.

INSTRUlmNT ERROR AND CORRECTION:

Ca) Collimation error; check before use and equalise sights.

(b) Under sensitive bubble.

(c) Errors in staff graduation; check.

(d) Loose tripod head.

(e) Telescope not parallel to bubble tube - Permanentadjustment.

(f) Telescope not at right angles to the vertical axis -Permanent adjustment.

LEVELLING USING A GRIDThis method of levelling is commonly used and is shown

set out in Fig.6. A grid pattern of lOmetre squares is setup over the site which can be pegged out off a chain lineand setting up the level at station A and by taking readingsin sequence a,b,c and d etc. an accurate way of levelling asite.

31

LEVELLING USING A GRID

r 0

"7k ,b11 m~o.

/f e d

-+----~----~--~~--~----~--~-MARTINS lANE

Fig 63~

LAND MEASUREMENT

BASIC PRINCIPLESThe basis of all land measurement is the use of a base

line and fixed points from which measurements can be taken.The following examples are used as basic principles for allsurve;ying methods.

1. RIGHT ANGLED CO-ORDINATES. A

x z YK ~Point A is located or fixed by the distance XZ along the

line XY measured at right angles to the line.It is mainly used for measuring boundaries and buildings

along a chain line, and is commonly known as taking rightangled offsets.

2. FOCAL CO-ORDINATES.

x yPoint A is located or fixed by measuring from X-A and

Y-A along a known chain line XY. This is quite often usedfor fixing station points in order to set up another chaini.e. XA.

3

J. ANGULAR CO-ORDINATES., 'A' /

x z r YPoint A is located or fixed by measuring the angles ol

and 'at points Z and R along a chain line XY. Where theangles intersect point A is located. This method is used aslines of intersection in Theodolite, plane table and compasssurvey work.

4. POLAR CO-ORDINATES.A

YPoint A is located or fixed by a known point Z along a

chain line XY and measuring the distance ZA together withangleo(. A method used in radiating lines on a plane tableand locating points generally.

4

AREAS & VOLUMES

AREASTrianglesArea = base x height

2

Corrmonly used in surveyingwhen lengths of sides areoften only values S ~known , 2

b

Area = / s( s-a ) (s-b )(S-C)a

Lengths of two sides and included knownane;le.

b

C

Ac

Ba

Area = ~ - aesinL = _be sin A222

Trapezium

5

The parallelogram

area =(a x h)

D~ a~ ~

Side8 included ~ known but not h.Area = ab Sin A or ab Cos B.

IRREGULAR FIGURES

Simpsons rule

A a B

~ssume that the bound ries are parabolic in shape and is mostEccurate for normal survey conditions. Can be used for VOLUJlr:ESif areas are substituted for ordinate lengths.

Y7

Odd number of ordinates.Even number of spaces.

j (width of strip) x [SUP.1 of Ls t and last or(hm,te]+ (twice sum of other odd ordinates) + (4 times sur,of even ordinates.)

Area

Are x [(y + v ) + 2(" +v ) + 4(V2+YA~+Y6)J_ '1 v7 "3 v r.; er L!3 ~ /

6

Trapezoidal rule

sed when there are any nu _ber of or-d i nat s or height s,-ay be used for volumes if are~s of sections are substituted

for ordinate lengths.Area = Interval (half sum of 1st and last ordinate + remaining

ordinates.)

Prismoidal formula

Al and A2 areas of ends.

Am are of middle 08ction.L over all distance between end sections.

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PLANE TABLE SURVEYING

Plane Table Surveying is a ouick method of measuring areasor sections of land. All of the work is carried out on ~iteby the Surveyor. It is not very often used as a practicalmethod of surveying for reasons of general accuracy andweather conditions in this country but it is very useful onmore drier climates. There are four main methods a) Radiation,b) Intersection, c) Resection, d) Traversing.

EQUIPMENTTo carry out a Plane Table Survey you will need a drawing

board on an adjustable tripod with rotating head. A smalllevel i.e. boat level with a compass to orientate the survey.An Alidade sighting straight edge, plumbing fork and plumbbob with stationers pin. Ranging poles, pegs and arrows withsteel measuring tape or chain. Some of these items are shownin Fig.1.

RADIATION METHODTo illustrate the method of Plane Table Surveying Fig.2.

shows a typical building site to be surveyed.Set up the Table in the centre of the site and level board

ensuring that all aspects of the site can be seen. Locate allother points i.e. change of boundary lines, positions of.anholes, gates, poles, trees etc. Then using the Alidade

sight onto the fixed points measure the distance from thecentre peg marked on the ground. By using a suitable scaledraw in the radiated line on the paper fixed securely to theboard from the centre pin which should be directly plumbed inover the measuring peg on the ground. When carrying out thisprocess the board should be clocked into position untilEiBhtings and measurements can be taken in sequence A,B,C etc.for the whole of the site. If this procedure is carried outcarefully then a reproduction of the site will be recorded tosc~le onto the board.

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