Surveying

Co tents

Introduction

Basic principles

Plane Table Surveying

Chain Surveying

levelling

Tables

page

1

3

8

11

'9

33

PIN

EQUIPMENT

BOAT LEVEL

ALlDADE

o

TRIPOD

PLU

M

B

BOB

Fig 1

PLANE TABLE SURVEY

RADIATION METHOD

Factory

---,,\

MARTINS

LANE

A PLAN OF A TYPICAL SITE

Fig 2

ID

CHAIN

SURVEYING

Chain Surveying has long been established as the easiest an basic form of land mea$urement and is still in common use. 3ased on triangulation and consisting of carrying out the survey in the field and plotting the survey to scale in the drawing 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 a straight 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.

EQUI

PMENT

The 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 of E eel wire and great care should be taken when folding so as ~o avoid entanglement and bending the links. When the chain is 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 are

out stret ched properly. There are two other chains used these being the Gunter Chain which is 66 feet in total length with 100 links of 7.92 inches, and the Engineers Chain 100 feet in length and

:.

~

E

_00 links each a foot long and marked at 10 foot i:r:tervalsv:ith tallies accord.ingLy,

Tapes

These are made of steel being the most accurate and being r-eI'er-r-ed to linen tapes. They are cornmon.l y in lengths of 10, 20 and 30 metres and are used to measure offsets to the main chci.nline.

EQUIPMENT

90

THE METRIC CHAIN

TAPE

CHAIN

ARROWS

"g

3

((

RA

N

GI

N

G

POLES

POLE SUPPORT

/

.,

.

e'

12

ArmlW

S

.-.•. 0':c are used to mark the end of each chain line and are JOOmm 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_doak 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 poles

etc.

e afore mentioned are illustrated in Fig.J.

orocedure iE to make a reconnaisance of the site the 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 is

C"~:.~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 before u~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 greater

r.=-'''''-:'_'''''''~:' or the J:4:5 Triangle rule employed using a tape. ractical nature of the survey has been carried - ~r_e::ullvchecking that all the information required has

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

RECO

NN

AISSA

N

CE & SETTING OUT STATIONS

The S

·

e

_.ClllJjAP ,.(~~. _

Fig 4

CH

A

I

N

SURVEYI

N

G

intermediate

ranging

pole

SETTI

N

G UP CHAI

N

LI

N

E

Fig 5

CLIN

OMETER

_~s ~ strument is used for measuring slopes of 3' or is simply illustrated below. By firstly viewing

~nstrument on the horizontal plane the instrument

and focussed onto the ranging pole up the

ope 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

CHAI

N

SU

RV

EY

S

L

OPING

SITES

To measure "Leg" slopes greater than o 3 , measure convenient horizontal distances, plumb down to ground level to fix point from which to take next measurement.

B

A

~e of slope with CLIlWJ·::ETER''0(11

Trigonometry AB=AC

C

o

s

e

{.

measure slope

----

_--

_---

--

-

->

-

-....----

--

--

---

_-

_--

_R

_AN

_GI

_N

_{G O}

_V

_{ER HILLS}

--

--

-CL

ES

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.

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 -!: nat AC=CD. DE at Rt. 1s to AD, wi th E.C.B. on straight ::"enAB =DE.

E

Y

OF LAKE OR WOOD

- -~ fraJework of chain lines _= area and triangulate - _-ies across the corners _:'e'; C:- IN TRAVERSING.

18

I TRODUCTION

This book has been set out to illustrate the fundamental

basis of land measurement and procedures to adopt when

surveying areas of land. The actual practice of carrying

out surveys has not changed much over the years with only

perhaps the refinement and advanced equipment now in use.

Wost of the procedures detailed in this publication are in

corr~on practice and will give a good grounding to

Architectural, Surveying and Building students.

It is emphasised t.at only practice in the field will

give a good and thorough understandinG of the methods

outlined here and the key being accuracy in performance.

LEVELLING

___ ~asic instrument for levelling is the surveyors

.••-:;,_<::;;:;.=- __e '!hichis an adaption of Keplers telescope ernployang

- __-ex Lenses which produce a real image and line of

_ line of collimation (i.e. principal axis) and will

- seussed 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 wlrich is collimated in metres and Readings of course will be inverted, this will be

ater.

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

=_:::'onof transparent material bounded by either plane

e:'surfaces.

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

{fJR/A./CIA9L IlxIs Or al..5.

Fig 1

fJL!J,UO COA./c4V£

right angles to the two parallel tangentc: of the

urfaces of the lens.

re

on the principal axis whose distance from the tRO

_ :'s proportional to their radii.

- -~~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 as

e-. ';;th ai 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 a

he principal axis called the "principal focus"

- ::'~:::". The distance from this point to the optical

-::e :ens is termed the "focal length" of the lens.

Fig

2

ib.IS, ~ c ~ ex lens ~ill produce an image on a screen T_is imat;e is termed a "Real Image". ens however causes the light rays to diverge pr-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 -_,eexpression I + + + ••••••••••• :-C~_ length of the combincation, or, compound lens, - ~!" " ov:n as the "jiowe r" of the lens. I etc. fJ' the focal length of individual lenses.

20

Production of a

n

image

An object being viewed through a lens is considered to

consist of a number of connected points, each radiating tV10 rays of light; one ray passing through the optical centre of the lens without being refracted, the other, parallel to the principal axis, refracted through the focal point, both intersecting to produce an inverted "real image" (See Fig.3.)

v

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~KA &JUc, VltW£D f

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focal length f U for a lens. There is a definite relationship between the

and the object distance V to the image distance This is expressed as: I I I

f

=

V +

11

and I 1 I

f

=

V U for a convex lens. for a concave lens (where f is negative) As the image must be produced on the same plane as the crOLS hairs of the telescope of surveying instruments, and the

distance from object to lens will vary causing a proportional variation in value U, it is essential to provide adjustment of

the lens by a focussing mechanism.

A single lens hov:everpossesses a number of faults, the two i portant ones being: (a) Chromatic aberration; v!hite light is split into its co ponent colours on refraction, terr-:ed"dispersion", and due to differing angles of refraction for each colour the image tends to be blurred and surrounded by a halo of colours. This is usually overcome by using two lenses of different material, e.g. one of crown glass and one of flint glass. (b) Snherical berrationj Thic is caused by various rays of liGht fIling on the lens not beine;r-e f'r-ac ted to pass exactLy thr-oughthe SC:.T:fioceal point. ~'l)sif'auIt is controlled by using thin Leris es and restrictine;the object to be viewed to an area close to the princip~l axis of a flc:..cturvature lens.

2

1

The telescope

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

collimation passing through the optical centres of the lenses

and the cross hairs. The e epiece magnifies both the real

image and the cross hairs in the same proportion as these are

both on a common plane. The eyepiece is usually the Ramsden

type, consisting of two pIano-convex le~ses mounted a short

distance apart in a self-contained case, which is threaded on

the outside to allow it to be screwed f'orwar-d or back in the telescope body to bring the cross hairs and image into clear focus. This arrangement of lenses reduces spherical aberration.

The object glass is usually a compound lens to reduce chromatic aberration.

Focussing

) /MIlCr~Fo.(?N/£D BY #£' PIECt. I'12/AJC /P4L.. 4;<15. j.!1../£ e>,r COLJ.IMI17IoA/ 1..11./&o.t: SI(jIlr:

Fig 4

Two forms of focussing mechanism are used to bring the

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

(a) External focussing: The body of the telescope is made

of two concentric close fittinG barrels, the object

glass mounted in one and the eyepiece and cross-hairs

in the other. A rack and pinion mechanism operated by

the "focussing screw" advances or retracts one tube in

relation to the other, thus increasing or reducing the

distance between object glass and eyepiece/cross-hairs.

This method was common on older instruments and is more

accurate for tacheometry purposes, but has the

disadvantage that wear on the tubes may allow entry of water, dust, etc., and impair the efficiency of the

instrument.

Cb) Internal focussing: A double concave lens mounted on ()

frame is fitted inside a one piece telescope body

between the object and eyepiece lenses. The frame

pocition is adjustable by means of a rack and pinion,

as before, which slides the lens tov:ards or away from

the object glass.

The concave len disperses the light rays from the

object glass to greater or lesser degree depending on

the position of the lens and thus allows focussing of

the image on the cross-hairs. The disadvantage of this

method is the loss of brilliance due to the extra lens.

Cross-hairs

Originally, spiders yeb was used, but these broke easily

and were difficult to replace. Today, very fine lines are

etched on a piece of very thin optical glass fastened to a

"reticule", forming an interchangeable capsule which fits into a flanged metal ring called the "diaphragm", held in the telescope barrel by four capstan headed screws - which should

only be touched when changing or making major adjustments to the cross-hairs.

Parallax

This term refers to relative motion between the object and

the cross-hairs when the eye is moved to and fro across the eyepiece, and means that the image and cross-hairs are not on the same plane. To eliminate parallax a piece of white paper

is held in front of the object lens and theeye-piece moved in or out until the cross-hairs stand out clear and black. The telescope is then focussed on the object and tested for

parallax again, the procedure being repeated if necessary until the parallax is eliminated.

The spirit level

Cormnonlyfastened to the ba.r-r-e I of the telescope on a levelliriginstrument, but usually on the top plate of a

Theodolite. The more sensitive spirit-levels are barrel

shaped curved glass tubes, with the less sensitive only a

portion of the surface is curved, when thee'termed non

-reversible levels. The glass tube is filled with ether or

alcohol with a sm2.11air space left to form a bubble. These fluids are less viscous than water, ~nd have a much lower freezing point, but a greater ey-pansion,so that a level left in very hot sun may burst.

The top surface of the tube has graduations etched on it

which aid in centralising the bubble in the centre of its run. The sensitiveness of the bubble is defined as the amount the

horizontal axis of the tube has to be tilted to cause the bubble

to move from one graduation mark to the next, e.g. 1 division

)0 sec. means a tilt of )0 sec. of arc above the horizontal

v.LlL cause a "run" of one graduation.

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 capstan

headed screws which alLov the tube to be adjusted so that it

loneitudinal axis is paralle to the principal axis of the

Telescope.

By this means one can adjust the instrument so that the

line of collimation is horizontal, i.e. at right a~gles to the

plane of gravity acting at the centre of the instrument: Do

not adjust the capstan screws unless making a major correction.

The centralising of the bubble may be observed in different

ways. On some instruments the tube is viewed in a rnirror

hinged to an angle of about 450• In other cases an internal

mirror may be used, or a right angle prism, to give the

surveyor an image of the bubble in the eyepiece so that he does no~ have to move round the instrument.

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

The circular or "cats eye" bubble is inferior in accuracy

to the level tube but gives an approximate level plane for

initial "C'uickset"levelling purposes.

Types of levels

DU.DV Level: The simplest form of level consists of a bubble tube attached to a telescope which is rigidly fixed

to a horizontally rotating centre post and top plate, in its

turn connected to a bottom plate by three or four levelling

foot screws, which can be adjusted to bring the spirit

lev~l and telescope axis horizontal.

T~o conditions are essential for accurate work.

1. The axis of the bubble tube must be parallel to the

axis of the telescope, i.e. line of collimation.

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

instru ent.

Tilting Level or Quickset Level: An improvement on the

Dumpy as the telescope can be pivoted in the vertical

plane by means of the tilting screw under the eyepiece end

of the telescope. It is only necessary to set the

instrument to an approximate horizontal plane by

reference to the "cats eye" bubble, the telescope being

brought level for each sighting by using the tilting scre~.

)

example

Precise Level: This is a development of the now almost

obsolete Wye level and the Tilting level.

The telescope tube may be tilted and also revolved in its

mountings so that b taking the mean of two readings on

the same station a true reading may be obtained, this

compensating for any error in the collimation of the instrument.

example

Terms used in levelling

Bench rark: A fixed point on the earth's surface whose

level above Ordnance datum is known.

Ordnance datun.e r~eansea level to which all other levels

and bench marks are related.

Back sight: The first sight taken from a given level

position.

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

Intermediate sight: Any other sight taken from this level position. HeiGht of Instrument: (H. of I). The height of the line of collimation above the datum. (i.e. si ht line or principal axis of telescope.)

25

Reduced level: (R.

=

.

.

Calculated height or level of a

poin a 0 e or below the datum.

Change Point: The point at wlri ch both a foresight and

then a backsight are taken (i.e. when the level changes position.)

METHOD

Setting up the level

1. Open tripod legs to 600 and press the feet firmly into ground.

2. Note how instrument is packed in the box before

removing and lift out carefully, never by the telescope tube.

3

.

Screw firmly onto tripod head; never crossing the threads.

4. Roughly level the instrument y adjusting the tripod

legs, complete adjustment by means of the footscrews,

i.e. bring the bubble to the centre of its run.

plan

c:; ~

.

axis at ric;ht of ent: Check that there is no play on the axis of the

instrument. Turn telescope over a p~ir of footscrews

o

and level-up. Then rev rse tube through 180 • If the bubble runs off centre bring it halfway back with

footscreVls and the balance of the way with the capstan he ded screws on the bubble tube.

Corrections

Curvature: as the eart.h is curved, a horizontal sight does not give the true relati e heights of two points over a long sighting distance. See Fig.6.

.

As C is so small cor.:paredto 2R it is ignored and the expression is written thus _X2 2R = correction. Distance 2 d2 i.e. curvature correction measured or Diameter of Earth 2R

Refraction: differin~ atmospheric conditions cause the

rays of light entering the telescope to be refracted, i.e. bent, towards the earth's surface to greater or lesser degree, so that on a long sight the reading seen on the staff is not on a true horizontal line but below it and nearer to the earth's surface than it is believed to be. This error due to refraction partly offsets the error due to curvature. As an average figure it is assumed that the error due to refraction is 1/7 that of curvature and in the opposite direction.

The combined correction for curvature2and refraction is usually quoted as a deduction of 6 d

7

x 2R from.the staff readlng.

R

Fig 6

27

For short sights t::&ci::ere:!1ceis so small t11Citit De.' be ignored, but in exact Ieve:l~~ sights should not exceefia

quarter of a mile to a Ol ::"euncertainty caused by these

errors. By taking back a.. fore-sights to staff positions at

nearly equal distances fro _t:helevel these faults may be

consicieredcancelled and are not calculated in normal

levelling operations.

o

,,/1 /)/S7,tftJCc~ ~ r

1

~

(

y

----

f

,

--..

1

-

J

-

--./'

{

Co Jpound Levelling: in whi.ch the levels are obtained only

by changing the position of the instrument as one follows the undulations of the ground in a long line of levels, or to

obtain clear sights which <::.rothe erwise obscured by obstacles.

Therefore there will be:

Forms of levelling

Simple 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

c

I,-.

,

(a) Kore than one line of colliDation. 2'/0

F

(b) A bo;;.cksie;alnd foresi1t ght for each change in instrument position.

A

I" -,J

F

_yl. ~~~---~.--------~r--~O~~/~~~~~--~~~l----~~--_ --l~· '( 1 1 '1 1 (c) Separate groups of intermediate sights reI ted to different instrument positions.

Fig 1

1-70 .--- -.{)O 2'00.

28

L

AN

D

SU

RV

EYI

N

G

GENERALLY

The main function of carrying out a practical land survey is to ascertain as accurately as possible the size and shape of building sites, fields or other areas of land masses. They may have on them ponds, buildings or include

other features such as ditches, streams and trees etc. which

may 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 be

important to·know how the site slopes for which you will need to carry out a level survey. Basically it is forming

a three dimensional picture of a particular area of land

with points of elevation marked on it so that vertical

can be taken through showing planes of elevation.

There are various methods of gathering this information

which will be illustrated and explained in this book. It will be necessary to have knowledge of geometry and a good

understanding of mathematics in order to plot and calculate

information gathered by the practical survey.

Experience and practical knowledge can only be gained by

actually carrying out the methods and procedures described in the field.

There are two basic methods of land measurement in building Plane Table Surveying and Chain Surveying, these will be

discussed and illustrated more fully in the following pages

of this book.

Other methods include the use of the Theodolite which is

used for measuring horizontal and vertical angles. This is

used mainl:y in Civil Engineering work i.e. road

construction etc. where greater land masses and distances are involved.

Over larger areas of land the curvature of the earth's

surface will have to be taken into account and is known as

Geor'ieticSurveyine;.It is used in Ordnance Survey work and

is a specialised branch of land survey work.

BO

O

K

I

NG

There are two forms of booking down level readings,

Collimation also known as Height of Instrument and Rise and

Fall method.

Rise

&

Fa

ll

Method

Using Fig.l. to illustrate this method the readings taken by the level are entered into columns of either Rise or Fall i.e. the reading A datum is entered into the back sight column with reading B entered into the foresight column. As B is smaller than A this denotes a Rise and the difference is entered into the Rise column and recorded as such with a

reduced level reading entered by adding to a datum figure of 100.00. for level at B.

Any intermediate Sights are entered into the appropriate column with reduced levels accordingly. Distances and

Remarks Columns are used to record change points and level points etc. This method makes it possible to check each page

by adding the Rise column and Fall column, the difference

should equal the difference between the backsight and foresight column as illustrated below.

RISE & FALL METHOD

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29

COLLIMA

T

ION METHOD

C

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mat

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th

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Again using Fig.l. to illustrate this method the

succeeding reading is subtracted from the last calculated collimation height i.e. reading at A is height of instrument being 102.00 after datum of 100.00 is added. This will then

give a Reduced level at each staff position.

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

Always check if possible back to the datum point by taking flying levels this will avoid a return visit to the

site.

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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 level station.

3.

Staff not held vertically.

4. Parallax - adjust.

5.

Instrument knocked or moved during backsight-foresight reading.

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 - Permanent

adjustment.

(f) Telescope not at right angles to the vertical axis

-Permanent adjustment.

LEVELLING USING A GR

I

D

This method of levelling is commonly used and is shown

set out in Fig.6. A grid pattern of lOmetre squares is set up over the site which can be pegged out off a chain line

and setting up the level at station A and by taking readings

in sequence a,b,c and d etc. an accurate way of levelling a

site.

LEVELLING USING A GRID

r

0

"7

k

,b11

m

~o.

/

f

e

d

-

+

-

-

-

-~

----

~

--

~

~--

~

----

~--~

-MARTINS

lANE

Fi

g

6

3~

LAND MEASUREMEN

T

BASIC PRINCIPLES

The 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 all

surve;yingmethods.

1. RIGHT ANGLED CO-ORDINATES.

A

x

z

Y

K

~

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 right

angled offsets.

2. FOCAL CO-ORDINATES.

x

y

Point A is located or fixed by measuring from X-A and

Y-A along a known chain line XY. This is quite often used

for fixing station points in order to set up another chain

i.e. XA.

J

.

ANGULAR CO-ORDINATES.

,

'/

'

A

x

z

r

Y

Point A is located or fixed by measuring the angles

ol

and 'at points Z and R along a chain line XY. Where the angles intersect point A is located. This method is used as

lines of intersection in Theodolite, plane table and compass

survey work.

4. POLAR CO-ORDINATES.

A

Y

Point A is located or fixed by a known point Z along a chain line XY and measuring the distance ZA together with angleo(. A method used in radiating lines on a plane table

and locating points generally.

AREAS & VOLUMES

AREAS

Triangles

Area

=

base x height

2

Corrmonlyused in surveying when lengths of sides are often only values

S

~

known , 2

b

Area

= /

s( s-a )(s-b

)(S-C)

a

Lengths of two sides and included known ane;le.

b

C

A

c

B

a

Area

= ~ -

aesinL

=

_be sin

A

222

Trapezium

The parallelogram

area =(a x h)

D

~

a~

~

Side8 included ~ known but not h.

Area = ab Sin A or ab Cos B.

I

RR

EGU

L

AR FIGURES

Simpsons rule

A

a

B

~ssume that the bound ries are parabolic in shape and is most

Eccurate for normal survey conditions. Can be used for VOLUJlr:ES

if areas are substituted for ordinate lengths.

Y7

Odd number of ordinates. Even number of spaces.

j (width of strip) x [SUP.1 of Lst and last or(hm,te]

+ (twice sum of other odd ordinates) + (4 times sur, of even ordinates.)

Area

Are x_{_}

[

(

y

_'1 + _v7v ) + 2("_"3+v_{v r.;}) + 4(V2_er+YA~L!+Y6)J

3 ~ /

Trapezoidal rule

sed when there are any nu _ber of or-dinat s or heights, -aybe 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.

7

PLA

N

E TABLE SURVEYI

N

G

Plane Table Surveying is a ouick method of measuring areas or sections of land. All of the work is carried out on ~ite by the Surveyor. It is not very often used as a practical

method of surveying for reasons of general accuracy and weather conditions in this country but it is very useful on

more drier climates. There are four main methods a) Radiation,

b) Intersection, c) Resection, d) Traversing.

EQUIPMENT

To carry out a Plane Table Survey you will need a drawing board on an adjustable tripod with rotating head. A small

level i.e. boat level with a compass to orientate the survey. An Alidade sighting straight edge, plumbing fork and plumb bob with stationers pin. Ranging poles, pegs and arrows with steel measuring tape or chain. Some of these items are shown in Fig.1.

RADIATION METHOD

To 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 all other 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 the

centre peg marked on the ground. By using a suitable scale draw in the radiated line on the paper fixed securely to the board from the centre pin which should be directly plumbed in over the measuring peg on the ground. When carrying out this process the board should be clocked into position until

EiBhtings and measurements can be taken in sequence A,B,C etc.

for the whole of the site. If this procedure is carried out carefully then a reproduction of the site will be recorded to

sc~le onto the board.