INDEX

1. INTRODUCTION

2. RECONISSANCE SURVEY

3. ANGLE MEASUREMENT

4. LEVELLING

5. TRIANGULATION

6. TACHEOMETRY

7. PLANE TABLE

8. CONTOUR PLOTTING

9. OBSERVATION TABLES

1.INTRODUCTION

Surveying is the art of determining the relative positions of points on, above or beneath the

surface of the earth by means of direct or indirect measurements of distance, direction and

elevation. It also includes the art of establishing points by predetermining angular and

linear measurements. The application of surveying requires skill as well as the knowledge

of mathematics, physics, and to some extent, astronomy. It is a technique of preparing the

map of an area. In all Engineering Projects the preparations of accurate plans and sections is

the first necessity.

In this survey camp, i.e. in Survey Camp 2009(Dec 10 – Dec 23), we got the project,

“TOPOGRAPHICAL MAP OF PEC”, in which we have to plot the prominent features of PEC

on the map with the help of various surveying techniques. Topography is meant by the

shape or configuration of the earth’s surface. The basic purpose of topographical map is to

indicate the three dimensional relationships for the terrain of any given area of land. Thus,

on a topographic map, the relative positions of the points are represented both horizontally

as well as vertically.

To get a comprehensive idea of the area, we explored the area looking in prominent points/

features that we have to show on the map and also we looked for any difficulty that we

might encounter in future while plotting the points on the sheet. This type of process of

exploring the area in detail and looking for points where we can set our instrument to get

the points on sheet is known as Reconnaissance.

After reconnaissance, we got the rough map of the area and the points where we will set our

instrument i.e. instrument stations.

We first selected one instrument station from where we wanted to commence our work,

but, the problem was that we were not aware of the elevation of that point w.r.t. mean sea

level (Reduced Level of that point), as with the help of that R.L., we have to find out and plot

the R.L of points that we have to show on the map.

So, for that purpose, we have gone to Regulatory End of Sukhna Lake, whose R.L. was

known to us, and which was approximately 3 Kms from our college. With the help of

Levelling Instrument, we got the R.L of the points that were in the way from Sukhna Lake to

College. So, finally we got the R.L of the point from where we have to commence our work.

In college, we used the instruments like Total Station, Plane Tabling with telescopic alidade

to get the R.L of various points and to plot those points on the sheet.

CAMP SITE

PEC MAP

2.RECONNAISSANCE     SURVEY

A  reconnaissance survey provides data that enables design engineers to study the

advantages and disadvantages of a variety of routes and then to determine which

routes are feasible. You begin by finding all existing maps that show  the  area  to  be

reconnoitered.  In  reconnaissance, studying existing maps is as important as the

actual fieldwork. Studying  these  maps  and  aerial photographs,  if  any  exist,  will

often  eliminate  an unfavorable  route  from  further  consideration,  thus saving

your reconnaissance field party much time and effort. Contour  maps  give  essential

information  about  the relief of an area. Aerial photographs provide a quick means

for preparing valuable sketches and overlays for your field party. Direct aerial

observation gives you an overview  of  an  area  that  speeds  up  later  ground

reconnaissance  if  the  region  has  already  been  mapped. Begin the study of a map

by marking the limits of the area to be reconnoitered and the specified terminals to

be  connected  by  the  highway.  Note  whether  or  not there are any existing routes.

Note ridgelines, water courses,  mountain  gaps,  and  similar  control  features. Look

for  terrain  that  will  permit  moderate  grades without   too   much   excavating.

Use   simplicity   in alignment and have a good balance of cuts and fills; or use a

profile arrangement that makes it possible to fill depressions with the cut taken

from nearby high places. Mark the routes that seem to fit the needs and that should

be reconnoitered in the field. From the map study,  determine  grades,  estimate  the

amount  of clearing  required,  and  locate  routes  that  will  keep excavation to a

minimum by taking advantage of terrainconditions. Mark stream crossings and

marshy areas as possible  locations  for  fords,  bridges,  or  culverts. Have  the

reconnaissance  field  party  follow  the route or routes marked earlier during the

map study. Field  reconnaissance  provides  you  with  an  opportunity for checking

the actual conditions on the ground and for noting  any  discrepancies  in  the  maps

or  aerial photographs. Make  notes  of  soil  conditions, availability of construction

materials, such as sand or gravel,  unusual  grade  or  alignment  problems,  and

requirements   for   clearing   and   grubbing.   Take photographs  or  make  sketches

of  reference  points, control   points,   structure   sites,   terrain   obstacles,

landslides,   washouts,   or   any   other   unusual circumstances. Your

reconnaissance survey party will usually carry lightweight instruments that are not

precise. Determine by compass the direction and angles. Determine the approximate

elevations by an aneroid barometer or altimeter. Use an Abney hand level

(clinometer) to estimate elevations and to project level lines. Other useful  items  to

carry  are  pocket  tapes,  binoculars, pedometer  and  pace  tallies,  cameras,

watches,  maps, and  field  notebooks. Keep design considerations in mind while

running a  reconnaissance  survey.  Remember  that  future operations may require

further expansion of the route system presently being designed. Locate portions of

the new route, whenever possible, along roads or trails that already exist. Locate

them  on  stable,  easily drained, high-bearing-strength soils. Avoid swamps,

marshes, low-bearing-strength soils, sharp curves, and routes  requiring  large

amounts  of  earthmoving. Keep the need for bridges and drainage structures to a

minimum. When the tactical situation permits, locate  roads  in  forward  combat

zones  where  they  can be concealed and protected from enemy fire. The report you

turn in for the reconnaissance field party must be as complete as possible; it

provides the major data that makes the selection of the most feasible route  or

routes  possible.

3.ANGULAR MEASUREMENT

Surveying and navigation often rely on the measurement of two phenomena in

order to determine position, those of distance (already covered in lectures) and

direction or bearing. These lecture notes will introduce the concept of bearings and

cover the instrumentation that has been developed over the centuries to facilitate

the determination of relative and absolute 'bearing'. In order to start, we will look at

the definition of some terms specific to the determination of direction.

3.1 Definitions:

Directions: - Simply that, a direction (over there).

Bearings: - A direction relative to a datum

Whole-circle bearings: The direction of survey lines is generally expressed as an

angle measured from a reference meridian, generally north, commencing from 0

degrees (0°) and increasing clockwise to 360 degrees (359°59'60"). Bearings are

never expressed as "North, X degrees East".

Angles: - The arithmetic difference between two directions or bearings.

Reference meridians:

True north (through the geographic poles about which the Earth rotates)

Magnetic north (through which lines of magnetic flux pass)

Grid north - An arbitrary meridian (one adopted for a particular project) - a

mathematically determined value

Magnetic meridian: - The direction of the earth's magnetic lines of force. This varies

with date, time and locality.

Magnetic declination - The angle between the magnetic and true meridians.

Angle measurement is a fundamental part of surveying field observations, as the

combination of a direction and a distance gives a polar vector to a point and hence a

unique location of that point in space. The instruments that have been developed to

facilitate angle (or direction) measurement are the magnetic compass , the sextant

and the theodolite.

3.2 The Magnetic Compass

The Magnetic Compass is an instrument which indicates the whole circle bearing

from the magnetic meridian to a particular line of sight. It consists of a needle or

disc magnetised so that it will align itself with the direction of the Earth's magnetic

flux, and some type of index scale so that numeric values for the bearing can be

determined. See diagram below.

The magnetic bearing is related to true bearings as follows:

d = Magnetic declination (positive when

clockwise)

qt = True bearing

qm = Magnetic bearingqt = q m + d

3.3 Variations in Declination

The geophysical phenomena that generate the Earth's magnetic flux are still not

fully understood. It is known that magnetic north moves quite considerably over

time, and has even reversed polarity in prehistory. Some of the phenomena that

effect the direction of magnetic flux (and hence magnetic north) are known as

variations in declination and are as follows:

Variation Cause Amount of Dd

Secular variation Rotation of magnetic pole around

geographic pole.

In 1933 - 8°

Diurnal variation Effect of sun during the day up to 10' In 1970 -

9°59'E

Irregular variation Sunspot activity up to 5°

Irregular variation

(cont)

Electrical storm up to 5°

Conclusion: Magnetic north is generally too unreliable for use as a survey

datum!

3.4 Local Attraction

The needle of the compass can also be 'attracted' by metallic objects close to the

point of observation. These objects cause local aberrations in the direction of

magnetic flux, and give rise to an effect known as local attraction. These local

disturbances in the Earth's magnetic field are often due to large iron masses, electric

cables, fences, cars and so on. They tend to occur locally, and if detected can

sometimes be compensated for in survey procedures. Magnetic anomalies caused by

underground minerals are a problem for surveyors, but form the basis of many

mineral exploration techniques so the news is not all bad.

Where a closed traverse consisting of compass bearings and distances has been

performed around a parcel of land (see later) it is possible to compensate for the

effects of local attraction and to distribute 'angular misclosure'.

This will be covered in more detail later but in summary the procedure consists of:

i. measuring forward and back bearing of each line

ii. computing angles and angle misclosure

iii. (misclosure = [180°(n - 2)] - S angles) {¹(n-2) - S angles} )

iv. adjusting each angle by adding to each

v. recomputing bearings from adjusted angles. (The bearing of one line must be

known or assumed).

The presence or otherwise of local attraction can be determined from the difference

between a 'forward' bearing and a 'reverse' bearing observed from, and to, a station.

If I was to measure from Point A to Point B, and then from Point B back to Point A

the difference in the bearings should be 180°. Any variation in this in excess of what

would be expected from random error would be most likely due to local attraction.

Needless to say both forward and reverse bearings are always observed when using

a compass for traversing.

3.5 Compasses

There are two main types of magnetic compasses used in the field by surveyors

navigators and orienteers: the Sunnto type and the prismatic type, as well as

compass-theodolites. There are others like the gyro-compass which are used in

inertial navigation systems, however they will not be addressed here.

Both the Sunnto type and the Prismatic type are held in the hand for use, and are

therefor subject to poor centring and an unstable platform. The effects of this are

reduced over long sight lines, which, when combined with the vagaries of the

magnetic meridian, combine to make the compass a reconnaissance or inventory

tool only. Neither the instruments nor the basis upon which they work are

sufficiently stable for any sort of precision work.

3.6 Measuring Horizontal Angles With Total Station Instruments

• Horizontal angles are measured in horizontal planes.

• To eleminate instrumental errors and increase precision, angle measurements

should

be repeated an equal number of times in each of the direct and reversed modes, and

the

average taken.

In the notes

1. the identification of the angle being measured is recorded in column (1)

2. the value of the first reading of the angle is placed in column (2)

3. it is only recorded for checking purposes, the fourth (final) reading is tabulated in

column (3)

4. the mean of the four readings, which produce the final angle, is given in column

(4)

3.7 Measuring Horizontal Angles by The Direction Method

4. LEVELLING

4.1 General

The primary reference at water-level recording stations is a set of stable bench-

marks, installed in locations where their level should not change. Upon initial set-up

of a station, the levels of the relevant parts of the installation are established and

recorded by means of accurate levelling. At least every two years, the levels of the

staff gauges, sensor level, internal gauge, tower structure and benchmarks should be

measured relative to each other as a check that records are not in error due to bank

subsidence or other movement.

Accurate levelling is thus a particularly important part of site establishment,

installation and quality assurance. All staff shall be thoroughly familiar with its

theory and practice.

Levelling and surveying methods are also used for measurements of river channel

and lake configurations. Often, less accurate methods can be used for this work than

for water-level recording stations, although the techniques are common.

4.2 Definitions

Differential levelling is the term applied to any method of measuring directly with a

graduated staff the difference in elevation between two or more points.

Precise levelling is a particularly accurate method of differential levelling which

uses highly accurate levels and with a more rigorous observing procedure than

general engineering levelling. It aims to achieve high orders of accuracy such as 1

mm per 1 km traverse. A level surface is a surface which is everywhere

perpendicular to the direction of the force of gravity. An example is the surface of a

completely still lake. For ordinary levelling, level surfaces at different elevations can

be considered to be parallel.

A level datum is an arbitrary level surface to which elevations are referred. The

most common surveying datum is mean sea-level (MSL), but as hydrological work is

usually just concerned with levels in a local area, we often use:

An assumed datum, which is established by giving a benchmark an assumed value

(e.g. 100.000m) to which all levels in the local area will be reduced. It is not good

practice to assume a level which is close to the actual MSL value, as it creates

potential for confusion. A reduced level is the vertical distance between a survey

point and the adopted level datum. A bench mark (BM) is the term given to a

definite, permanent accessible point of known height above a datum to which the

height of other points can be referred. It is usually a stainless steel pin embedded in

a substantial concrete block cast into the ground. At hydrological stations rock bolts

driven into bedrock or concrete structures can be used, but structures should be

used warily as they themselves are subject to settlement. The locations of

benchmarks shall be marked with BM marker posts and/or paint, and recorded on

the Station History Form. A set-up refers the position of a level or other instrument

at the time in which a number of observations are made without mooring the

instrument. The first observation is made to the known point and is termed a

backsight; the last observation is to the final point or the next to be measured on the

run, and all other points are intermediates.

A run is the levelling between two or more points measured in one direction only.

The outward run is from known to unknown points and the return run is the check

levelling in the opposite direction.

A close is the difference between the starting level of the initial point for the

outward run and that determined at the end of the return run. If the levels have

been reduced correctly this value should be the same as the difference between the

sum of the rises and falls and also the difference between the sum of the backsights

and foresights.

Height of Collimation is the elevation of the optical axis of the telescope at the time

of the setup.

The line of collimation is the imaginary line at the elevation.

Orders of levelling refer to the quality of the levelling, usually being defined by the

expected maximum closing error.

Order Purpose Maximum close (m)

Precision order Deformation surveys 0.001 x km

First order Major levelling control 0.003 x km

Second order Minor levelling control 0.007 x km

Third order Levelling for construction 0.012 x km

Table Levelling closes

The accuracy requirements for water-level stations relate to the standards; for

further information refer to next section.

Change points are points of measurement which are used to carry the

measurements forward in a run. Each one will be read first as a foresight, the

instrument position is changed, and then it will be read as a backsight.

4.3 Equipment

The level, its tripod, the staff and the staff bubble are all precision items of

equipment upon which the accuracy of the work is highly dependent. They shall be

kept correctly calibrated, and be used and stored with care. Levels shall be carried

in vehicles in a padded box, case or shelf in addition to the normal case, and staves

shall be kept in a canvas or plastic sleeve to prevent damage to the face and entry of

dirt.

Levels

A level is basically a telescope attached to an accurate levelling device, set upon a

tripod so that it can rotate horizontally through 360°. Normally the levelling device

is a bubble, but modern ones incorporate a pendulum. There are three basic types of

level, shown in figure below.

(a) Dumpy levels

These are more basic levels often used in construction work. The telescope is rigidly

attached to a single bubble and the assembly is adjusted either by means of a

screwed ball-joint or by footscrews which are adjusted first in one direction, then at

90°.

(b) Tilting levels

This type of level is fitted with a circular bubble for preliminary approximate

levelling and a main bubble which is attached to the telescope. For each observation

(not setup) the main bubble is viewed through an eyepiece and the telescope tilted

by a fine screw to bring the two ends of the bubble into coincidence.

(c) Automatic levels

This more modern type of level is now in general use. It has a compensator which

consists of an arrangement of three prisms. The two outer ones are attached to the

barrel of the telescope. The middle prism is suspended by fine wiring and reacts to

gravity. The instrument is first leveled approximately with a circular bubble; the

compensator will then deviate the line of sight by the amount that the telescope is

out of level.

Staves

The levelling staff is a box section of aluminium or wood, which will extend to 3 or 5

m in height by telescoping, hinging or addition of sections. One face has a graduated

scale attached for reading with the cross-hairs of the level telescope. These faces can

vary in pattern and graduation; 5mm graduations should be the maximum for

accurate levelling of gauging stations.

Many staves used these days are of aluminium because of its durability. However

aluminium has a co-efficient of thermal expansion of 0.000023m/metre of

length/°C and this can cause some potential inaccuracies. For instance, "Survey

Chief" and "Brookeades" staves are standardised at 27°C, and in very cold weather

these staves could be as much as 3mm too short over their full length. For low

temperature work consult the temperature table for each staff which should be with

its "instruction manual" or printed on the staff itself.

Staff bubbles

These are generally a small circular bubble on an angle plate which is held against

one corner of the staff to ensure that the staff is held in a vertical position. If the staff

is not held vertical, the reading will be too large and may be significantly in error.

A staff bubble shall be used at all times. If one is not available, the "chainman" (staff

operator) shall rock the staff slowly back and forth about the vertical in a line

towards the instrument. The observer notes the smallest reading which will occur

when the staff is vertical.

4.4 Care of equipment

• ensure that tripod screws and hinges are kept tight.

• always transport the level in a padded box.

• when removing from the box lift it by the centre and not by the eyepiece or

objective end of the telescope.

• screw it firmly onto the tripod, whilst holding it in one hand (make certain that it is

not cross-threaded and that threads are compatible).

• when carrying the level tripod assembly in the field, support it over the shoulder

or, in bush, crooked over an arm with the telescope unclamped (i.e. free to rotate).

• automatic levels should not be carried in a vertical or near-vertical position, as the

compensator will swing about and be prone to damage.

• staves are too much of a precision item of equipment to be used in place of a

slasher, vaulting pole, etc.

• staves shall be transported in their protective cases to protect the face from

damage.

• wooden staves which become wet should be dismantled and dried out before

storing away.

• any moisture which is evident in an instrument must be allowed to disperse by

storing the level out of its case in a warm room. Should it persist after several days

the instrument may require specialist servicing.

4.5 Checking the level’s accuracy

Levels can move out of adjustment so that their line of sight (line of collimation) is

not truly horizontal. This will cause errors in readings which become greater as the

viewing distance increases. However if a backsight and a foresight are exactly equi-

distant from the instrument, the error in each sighting will cancel each other out.

This feature can be used to check the accuracy of a level by the following simple

method which is depicted in figure below

• install three pegs or marks firmly in the ground at distances of 30 m apart in a

straight line; the centre peg is only to mark the distance, but the outside two shall be

firm enough for reliable change points

• set up the level over the centre peg and read the staff on each of the outside pegs

in turn. Book these values and calculate the height difference. This will be a true

height difference, as the distances are equal and any errors will be self-

compensating

• set up the level about 4 m to the far side of one of the outside pegs. Read the staff

on the peg 4 m away and then on the one 64 m away. Book these values and

calculate the apparent height difference

• compare the two height differences; if the instrument is in adjustment (i.e. its

collimation is true) they will be within 5 mm.

A method for checking the level accuracy

If the instrument's collimation appears to be out, recheck by repeating the process.

Then, whilst setup at one of the outside locations, adjust the instrument (according

to the manufacturer's instructions) so that it reads the correct value on the far staff,

checking it against the near one. Two staves are useful for this.

This type of level check shall be carried out at least once per year, preferably just

prior to carrying out a round of station inspections. The details and results of the

checks shall be recorded in a numbered level book and be readily retrievable as a

quality record, and the date of this calibration check shall also be recorded in the

instrument inventory.

4.6 Levelling procedures

(a) Setting up

• Backsight and foresight distances should be approximately equal to avoid any

errors due to collimation, refraction or earth curvature.

• Distances must not be so great as to not be able to read the graduations accurately.

• The points to be observed must be below the level of the instrument, but not lower

than the height of the staff.

(b) Elimination of parallax

Parallax is the apparent movement of the image produced by movement of the

observer's eye at the eyepiece.

It is eliminated by focusing the telescope on infinity and then adjusting the eyepiece

until the cross-hairs appear in sharp focus. The setting will remain constant for a

particular observer's eye.

(c) Booking

• level books or loose-leaf levelling sheets shall be numbered and indexed in a

register.

• details of the site, work, date, observer, chainman, booker, weather, wind,

instrument and any other relevant items shall be entered.

• enter the first observation (which is on a known point) in the Backsight column,

and sufficient detail in the Remarks column to identify it. Enter the point's R.L. zero

from the site register or plate on the BM, etc.

• enter all other points on subsequent lines as intermediates except the point

chosen as the foresight. Identify them in the Remarks column as above. Enter the

foresight on a further line in the Foresight column.

• change the instrument to the next setup. Enter the following backsight on the same

line as the previous foresight but in the Backsight column.

• repeat the above procedure at each setup on the outward run then reverse it to

work back to the starting point on the return run. The furthest point out is treated

as for all other change points.

4.7 Reducing the levels

Two methods are in general use; the "rise and fall" method and the "height of

collimation" method.

The latter reduces levels relative to the instrument height. As it has inferior in-built

checks it should not be used and will not be covered here.

The "rise and fall" methods shall be used for reduction of all site levelling. Reduction

shall be carried out on site before packing up to ensure that the levelling has been

done correctly.

• calculate the rises and fall between successive points and book them in the

appropriate column (one can determine whether each shot is a rise or fall by the

following rule of thumb: a higher value on top denotes a rise; a higher value on the

bottom denotes a fall)

• add up the backsight and foresight columns for the entire traverse and note the

difference between them; this is the close

• add up the rises and falls for the entire traverse, and compare the difference

between them with the difference between the backsights and foresights; they

should be the same

• carry the reduced levels in the R.L. column down the page by adding or subtracting

the appropriate rise and fall values to the successive values of R.L.

The final value of the original starting point will differ from the original value by the

amount of the close.

If the levelling has been done correctly and all arithmetic reductions are correct, the

differences between total backsights and foresights, total rises and falls, and starting

and finishing R.L.'s should be the same. This difference is the close; and for site

inspection purposes it should be within ± 2mm or ± 6mm, depending upon which

water-level standard is being followed, ± 3mm or ± 10mm.

4.8 Level books

All levelling shall be booked in either level books or levelling sheets which shall be

retained as permanent records .Level books shall be numbered so that they can be

referenced on station history and inspection forms . They should be stored in fire-

proof storage as for original record. They should also include an index.

Levelling sheets shall be filed in time-sequential order in site files, and also need to

be infire-proof storage as for level books.

5.TRIANGULATION

This method—  triangulation —requires  that  distances  be measured only at the

beginning, at specified intervals, and at the end of the survey. Both the triangulation

method and the traverse method of control are based on the character of the terrain,

and not on the degree of precision to be attained; that  is,  each  system  is  equally

precise  under  the conditions   in   which   each   is   used.   Discussion   of

triangulation in this chapter normally is limited to triangles having sides less than

3,000 yards in length and to triangulation nets that do not extend more than 25,000

yards. The triangulation method is used principally in situations where the chaining

of distances is impossible or infeasible except with the use of electronic measuring

devices. Suppose you want to locate a point, say, point C, which is offshore; and the

measured baseline, AB, is located  on  the  shore.  In  this  situation  the  triangulation

method is used because the chaining of distances is impossible.  The  chaining  of

long  distances,  especially in rough country, also is not always possible; therefore,

triangulation is used to establish horizontal control in large-area   surveys. In   some

large-area   surveys   conducted   by triangulation,  you  must  consider  factors

involving  the curvature of the earth; hence, in such cases,  geodetic triangulation  is

involved.  Whether  or  not  the  curvature of the earth must be considered depends

upon the area covered  and  the  precision  requirements  of  the  survey. The  error

resulting  in  horizontal  measurements  when you ignore the curvature of the earth

amounts to about 1 foot in 34 1/2 miles. This means that in most ordinary

surveying,  an  area  of  100  square  miles  may  be plane-triangulated without

significant error. In this discussion  we  are  concerned  with  plane  triangulation

only. For a discussion of geodetic triangulation, you should refer to commercial

publications. This section contains information on the three types of  triangulation

networks  and  the  usual  procedure  for conducting a triangulation survey. Also

covered are primary and secondary triangulation stations, types of signals used in

marking triangulation stations, and checking for precision and locations of points.

5.1 Supervision and triangulation surveys

In triangulation surveys, the duties of the EA1 are those of party chief; that is, he

directs the triangulation survey. He keeps the triangulation notes and should be at

the  spot  where  any  important  measurement  is  made so that he can verify the

readings personally. He is responsible  for  selecting  triangulation  stations  and

erecting triangulation signals and towers. He determines the degree of precision to

be attained. He also performs the computations necessary to determine horizontal

locations  of  the  points  in  the  triangulation  system  by bearing  and  distance.

Triangulation is used extensively as a means of control  for  topographic  and

similar  surveys.  A triangulation system consists of a series of triangles. At least one

side of each triangle is also aside of an adjacent triangle;  two  sides  of  a  triangle

may  form  sides  of adjacent triangles. By using the triangulation method of control,

you do not need to measure the length of every line.   However,   two   lines   are

measured   in   each system—one line at the beginning and one at the closing of the

triangulation system. These lines are called  base lines and are used as a check

against the computed lengths  of  the  other  lines  in  the  system.  The

recommended length of a base line is usually one sixth to  one  fourth  of  that  of  the

sides  of  the  principal triangles. The transcontinental system established by the U.S.

Coast and Geodetic Survey (now the National Geodetic  Survey)  is  an example of an

extensive high-order triangulation network to establish control across the United

States.

Chain of single triangles.

5.2 Types of triangulation networks

In  triangulation  there  are  three  types  of  triangulation networks  (or  nets).  They

are  the  chain  of  single triangles, chain of polygons, and chain of quadri-

laterals. Chain of Single Triangles The simplest triangulation system is the chain

of single  triangles  shown  in   figure   15-15.  Suppose  AB is the  base  line  and

measures  780.00  feet  in  length. Suppose, also, that angle A (that is, the observed

angle BAC)  measures 98°54´ and that angle  ABC measures 32°42´. (In actual

practice you will use more precise values than these; we are using rough values to

simplify the  explanation.)  Subtracting  the  sum  of  these  two angles from 180°, we

get 48°24´ for angle  ACB. Next, solve for sides BC and AC by using the law of  sines

as  follows:

Now that you know how to find the length of BC, you can proceed in the same

manner to determine the lengths of  BD and CD. Knowing the length of  CDcan

proceed in the same manner to determine the lengths of CE and DE, knowing  the

length  of  DE, you  can determine the lengths of DF and EF, and so on. You should

use this method only when locating inaccessible points, not when a side of the

triangle is to be used to extend  control. In comparison with the other systems about

to be described,   the   chain   of   single   triangles   has   two disadvantages. In the

first place, it can be used to cover only a relatively narrow area. In the second place,

it provides  no  means  for  cross-checking  computed distances using computations

made by a different route. In figure 15-15, for example, the only way to compute the

length of BC is by solving the triangle ABC, the only way to compute the length of  CD

is  by  solving  the triangle  BCD  (using  the  length  of  BC  previously computed);

and  so  on.  In  the  systems  about  to  be described, a distance maybe computed by

solving more than one series of triangles. Technically  speaking,  of  course,  a

triangle  is  a polygon; and therefore a chain of single triangles could be called a

chain of polygons. However, in reference to triangulation figures, the term chain of

polygons refers to a system in which a number of adjacent triangles are combined  to

forma  polygon,  as  shown  in   figure   15-16 . Within each polygon the common vertex of

the triangles that compose it is an observed  triangulation station (which is not the

case in the chain of quadrilaterals described  later). You can see how the length of

any line shown can be computed by two different routes. Assume that  AB is the

base line, and you wish to determine the length of line  EF.  You  can  compute  this

length  by  solving triangles  ADB, ADC, CDE,  and EDF, in that order, or by solving

triangles  ADB, BDF,  and FDE, in that order. You can also see that this system can be

used to cover a wide territory. It can cover an area extending up to approximately

25,000  yards  in  length  or  breadth.

Chain of polygons.

6. TACHEOMETRY

6.1 Introduction

This method of survey consists of using either a level, theodolite or specially

constructed tacheometer to make cross hair intercept readings on a levelling staff.

As the angle subtended by the crosshairs is known, the distance can be calculated.

6.2 Definition

Tacheometry is an optical solution to the measurement of distance. The word is

derived from the Greek Tacns, meaning 'swift', and metrot, meaning 'a measure'.

Present day methods of tacheometry can be classified in one of the following three

groups. The last two groups will not be covered in these notes.

1. Stadia System: The theodolite is directed at the level staff and the distance is

measured by reading the top and bottom stadia hairs on the telescope view.

For further information about this process is provided in Theodolite

Tacheometry

2. Electronic Tacheometry: Uses a total station which contains an EDM, able to

read distance by reflecting off a prism.

3. Subtense Bar system: An accurate theodolite, reading to 1" of arc, is directed

at a staff, two pointings being made and the small subtended angle measured.

4. Optical Wedge system: A special theodolite with a measuring device in front

of the telescope s directed at a staff. One pointing of the instrument is

required for each set of readings.

There are two types of instruments used for stadia surveying. In the first type the

distance between the two stadia hairs in the theodolite telescope is fixed. In the

second type of equipment the distance between the stadia hairs is variable, being

measured by means of a micrometer.The most common method used involves the

fixed hair tacheometer, or theodolite.The notes below shows the calculation of the

distance (D) from the centre of the fixed hair tacheometer to a target.

From the diagram, triangles AOB, aOb are similar

OX=

U=

AB

Ox V ab

Also if OF = f = focal length of object lens

then 1/U + 1/V = 1/f (lens equation) and multiply both

sides by (Uf).

u = (U/V) .f + f

u = (AB/ab) .f + f

AB is obtained by subtracting the reading given on the staff by the lower stadia hair

from the top one and is usually denoted by s (staff intecept), and ab the distance apart

of the stadia lines is denoted by i. This value i is fixed, known and constant for a particular

instrument.

U = (f/i) .s +f

D = (f/i) .s + (f + c)

The reduction of this formula would be simplified considerably if the term f/i is

made some convenient figure, and if the term (f + c) can be made to vanish.

D = Cs + k

In practice, the multiplicative constant generally equals 100 and the additive

constant equals zero.This is certainly the case with modern instruments by may not

always be so with older theodolites.

The values are usually given by the makers but this is not always the case. It is

sometimes necessary to measure them in an old or unfamiliar instrument. The

simplest way, both for external and internal focussing instruments, is to regrad the

basic formula as being a linear one of the form:

D = Cs + k

a. On a fairly level site chain out a line 100 to 120m long, setting pegs at 25 to

30 metre intervals.

b. Set at up at one end and determine two distances using tacheometer or

theodolite, one short and one long. hence C and K may be determined.

i.e. D1 (known) = Cs1 (known) + k

  D2 (known) = Cs2 (known) + k

Distance Readings Intervals

  Upper

Stadia

Centre Lower

Stadia

Upper Lower Total

30.000 1.433 1.283 1.133 0.150 0.150 0.300

55.000 1.710 1.435 1.160 0.275 0.275 0.220

90.000 2.352 1.902 1.452 0.450 0.450 0.900

D =Cs + k

30.00 = 0.300 * C + k

90.00 = 0.900 * C + k

therefore C = 100 & K = 0

Any combination of equations gives the same result, showing that the telescope is

anallatic over this range, to all intents and purposes.

In order to avoid errors due to differential refraction of light through the

atmosphere, the lower stadia reading should not be too low on hot days, generally

not less than 0.5m. With respect to earth curvature both stadia readings are equally

affected and there is no effect on the value of the intercept. Correction for curvature

on the distance and level should be applied if the sight lengths are long enough.

The theory discussed so far, in The Stadia System, Measurement of Tacheometric Constants and

Refraction and Curvature, all applies to the situation where the staff is held vertically and

the line of sight of the telescope is horizontal. It is very seldom, however, that this

situation occurs in practice. Generally a theodolite is sighted to a level staff held

vertically (by use of a staff bubble), which gives rise to the situation below.

Since the staff is not at right angles to the line of sight of the instrument, the

intercept cut on the staff by the stadia hairs will be too large. Let the actual distance

between upper and lower stadia be s and the required projection of it at right angles

to IQ be s1

\ D = Cs1 + K, but s1 = s cos q

In practice, the slope distance D is not often required. What we really want is S, the

horizontal distance and V the vertical distance between the trunnion axis of the

telescope and the point of the staff cut by the centre hair.

Now S = D cos q

  = Cs cos2 q + k cos q

AlsoV =

D sin q

  = Cs cos q sin q + k sin q

 =

Cs sin 2q+ k sin q

  2

So now the horizontal distance S = Cs cos2 q + K cos q, and the vertical component is

given by V = Cs cos q sin q + K sin q. In practice these can be reduced to:

S = 100 s cos2 q and

V = 100 s cos q sin q

The difference in height between the two points is given by:

DH =HI + V - CL,

and the Relative Level (R.L.) of the point is given by

RL = RLA + HI + 100 s cos q sin q - CL

The use of these formulae gives the three dimensional location of the point. It is

quite easy to determine the coordinates of the point if the bearing is measured as

well as the staff intercepts and vertical angle, which of course is the standard field

procedure.

7.PLANE TABLE

7.1History

The earliest mention of a plane table dates to 1551 in Abel Foullon's "Usage et

description de l'holomètre", published in Paris.[3] However, since Foullon's

description was of a complete, fully-developed instrument, it must have been

invented earlier.A brief description was also added to the 1591 edition of Digge's

Pantometria.]The first mention of the device in English was by Cyprian Lucar in

1590. Some have credited Johann Richter, also known as Johannes Praetorius, a

Nuremberg mathematician, in 1610 with the first plane table, but this appears to be

incorrect.

The plane table became a popular instrument for surveying. Its use was widely

taught. Interestingly, there were those who considered it a substandard instrument

compared to such devices as the theodolite, since it was relatively easy to use. By

allowing the use of graphical methods rather than than mathematical calculations, it

could be used by those with less education than other instruments.

7.2 Plane table construction

A plane table cutaway.

This shows a plane table with part of the surface of the table cut away to show the

mounting on the tripod. The mount allows the table to be levelled. On the table, the

alidade with telescopic sight is seen

A plane table consists of a smooth table surface mounted on a sturdy base. The

connection between the table top and the base permits one to level the table

precisely, using bubble levels, in a horizontal plane. The base, a tripod, is designed to

support the table over a specific point on land. By adjusting the length of the legs,

one can bring the table level regardless of the roughness of the terrain.

7.3 Use of a plane table

In use, a plane table is set over a point and brought to precise horizontal level. A

drawing sheet is attached to the surface and an alidade is used to sight objects of

interest. The alidade, in modern examples of the instrument a rule with a telescopic

sight, can then be used to construct a line on the drawing that is in the direction of the

object of interest.

By using the alidade as a surveying level, information on the topography of the site

can be directly recorded on the drawing as elevations. Distances to the objects can

be measured directly or by the use of stadia marks in the telescope of the alidade.

7.4 Alidade

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Not to be confused with Adelaide.

A simple alidade for use with a ceiling projector

Several examples of alidade

An alidade (archaic forms include alhidade, alhidad, alidad) is a device that allows

one to sight a distant object and use the line of sight to perform a task. This task can

be, for example, to draw a line on a plane table in the direction of the object or to

measure the angle to the object from some reference point. Angles measured can be

horizontal, vertical or in any chosen plane.

The alidade was originally a part of many types of scientific and astronomical

instrument. At one time, some alidades, particularly those used on graduated circles

as on astrolabes, were also called diopters.[1] With modern technology, the name is

applied to complete instruments such as the plane table alidade.

Modern alidade types

A U.S. Navy sailor using a telescopic alidade.

The alidade is the part of a theodolite that rotates around the vertical axis, and

that bears the horizontal axis around which the telescope (or visor, in early

telescope-less instruments) turns up or down.

In a sextant the alhidade is the turnable arm carrying a mirror and an index to

a graduated circle in a vertical plane. Today it is more commonly called an

index arm.

Alidade tables have also long been used in fire towers for sighting the bearing to

a forest fire. A topographic map of the local area, with a suitable scale, is oriented,

centered and permanently mounted on a leveled circular table surrounded

by an arc calibrated to true north of the map and graduated in degrees (and

fractions) of arc. Two vertical sight apertures are arranged opposite each

other and can be rotated along the graduated arc of the horizontal table. To

determine a bearing to a suspected fire, the user looks through the two sights

and adjusts them until they are aligned with the source of the smoke (or an

observed lightning strike to be monitored for smoke).

7.5 Telescopic sight

Types

Telescopic sights are classified in terms of the optical magnification and the

objective lens diameter, e.g. 10×50. This would denote 10 times magnification with a

50 mm objective lens. In general terms, larger objective lens diameters, due to their

ability to gather larger amounts of light, provide a larger exit pupil and hence

provide a brighter image at the eyepiece. On fixed magnification sights the

magnification power and objective diameter should be chosen on the basis of the

intended use.

There are also telescopic sights with variable magnification. The magnification can

be varied by manually operating a zoom mechanism. Variable sights offer more

flexibility regarding shooting at varying ranges, targets and light conditions and

offer a relative wide field of view at lower magnification settings. The syntax for

variable sights is the following: minimal magnification – maximum magnification ×

objective lens, for example, 3–9×40.

Confusingly, some older telescopic sights, mainly of German or other European

manufacture, have a different classification where the second part of the designation

refers to 'light gathering power.' In these cases, a 4×81 (4× magnification) sight

would be presumed to have a brighter sight picture than a 2.5×70 (2.5×

magnification), but the objective lens diameter would not bear any direct relation to

picture brightness, as brightness is affected also by the magnification factor.

Typically objective lenses on early sights are smaller than modern sights, in these

examples the 4×81 would have an objective approximately 32mm diameter and the

2.5×70 might be approximately 25mm.

Optical parameters

Telescopic sights are usually designed for the specific application for which they are

intended. Those different designs create certain optical parameters. Those

parameters are:

Magnification — The ratio of the focal length of the eyepiece divided into the focal

length of the objective gives the linear magnifying power of telescopes. A

magnification of factor 10, for example, produces an image as if one were 10 times

closer to the object. The amount of magnification depends upon the application the

telescopic sight is designed for. Lower magnifications lead to less susceptibility to

shaking. A larger magnification leads to a smaller field of view.

Objective lens diameter – The diameter of the objective lens determines how much

light can be gathered to form an image. It is usually expressed in millimeters.

Field of view — The field of view of a telescopic sight is determined by its optical

design. It is usually notated in a linear value, such as how many meters (feet) in

width will be seen at 100 m (or 100 yd), or in an angular value of how many degrees

can be viewed.

Exit pupil — Telescopic sights concentrate the light gathered by the objective into a

beam, the exit pupil, whose diameter is the objective diameter divided by the

magnifying power. For maximum effective light-gathering and brightest image, the

exit pupil should equal the diameter of the fully dilated iris of the human eye —

about 7 mm, reducing with age. If the cone of light streaming out of the eyepiece is

larger than the pupil it is going into, any light larger than the pupil is wasted in

terms of providing information to the eye.

However, a larger exit pupil makes it easier to put the eye where it can receive the

light: anywhere in the large exit pupil cone of light will do. This ease of placement

helps avoid vignetting, which is a darkened or obscured view that occurs when the

light path is partially blocked. And, it means that the image can be quickly found

which is important when aiming at game animals that move rapidly. A narrow exit

pupil telescopic sight may also be fatiguing because the instrument must be held

exactly in place in front of the eyes to provide a useful image. Finally, many people

in Europe use their telescopic sights at dusk, dawn and at night, when their pupils

are larger. Thus the daytime exit pupil of about 3 to 4 mm is not a universally

desirable standard. For comfort, ease of use, and flexibility in applications, larger

telescopic sights with larger exit pupils are satisfying choices even if their capability

is not fully used by day.

7.6 Reticles

Rangefinder reticle.

Telescopic sights come with a variety of different reticles, ranging from the traditional

crosshairs to complex reticles designed to allow the shooter to estimate accurately

the range to a target, to compensate for the bullet drop, and to compensate for the

windage required due to crosswinds. A user can estimate the range to objects of

known size, the size of objects at known distances, and even roughly compensate for

both bullet drop and wind drifts at known ranges with a reticle-equipped scope.

For example, with a typical Leupold brand duplex 16 MOA reticle (of a type as shown

in image B) on a fixed power scope, the distance from post to post (that is, between

the heavy lines of the reticle spanning the center of the scope picture) is

approximately 32 inches (81.3 cm) at 200 yards (183 m), or, equivalently,

approximately 16 inches (40.65 cm) from the center to any post at 200 yards. If a

target of a known diameter of 16 inches fills just half of the total post-to-post

distance (i.e. filling from scope center to post), then the distance to target is

approximately 200 yards (183 m). With a target of a diameter of 16 inches that fills

the entire sight picture from post to post, the range is approximately 100 yards.

Other ranges can be similarly estimated accurately in an analog fashion for known

target sizes through proportionality calculations. Holdover, for estimating vertical

point of aim offset required for bullet drop compensation on level terrain, and

horizontal windage offset (for estimating side to side point of aim offsets required

for wind effect corrections) can similarly be compensated for through using

approximations based on the wind speed (from observing flags or other objects) by

a trained user through using the reticle marks. The less-commonly used holdunder,

used for shooting on sloping terrain, can even be estimated by an appropriately-

skilled user with a reticle-equipped scope, once the slope of the terrain and the slant

range to target are both known.

There are two main types of reticles:

Wire reticles

Etched reticles

7.7 Spirit level

A spirit level or bubble level is an instrument designed to indicate whether a surface

is level or plumb. Different types of spirit levels are used by carpenters, stone

masons, bricklayers, other building trades workers, surveyors, millwrights and

other metalworkers, and serious videographers.

Original spirit levels had two banana-shaped curved glass vials at each viewing

point and were much more complicated to use. In the 1920s, Henry Ziemann, the

founder of Empire Level, invented the modern level with a single vial. These vials,

common on most ordinary levels today, feature a slightly curved glass tube which is

incompletely filled with a liquid, usually a yellow-colored 'spirit' (a synonym for

ethanol), leaving a bubble in the tube. A spirit such as Ethanol is used due to its very

low viscosity. This provides an ideal element for a bubble to travel the tube quickly

and settle accurately with minimal interference generated from surface tension

between the transfer fluid and the glass housing. Most commonly, spirit levels are

employed to indicate how horizontal (level) or how vertical (plumb) a surface is.

Some are also capable of indicating the level of a surface between horizontal and

vertical to the nearest degree. The crudest form of the spirit level is the bull's eye

level: a circular flat-bottomed device with the liquid under a slightly convex glass

face which indicates the center clearly. It serves to level a surface in two

perpendicular directions, while the tubular level only does so in the direction of the

tube. The most sophisticated spirit levels are guaranteed accurate to five-ten-

thousandth of an inch (.0005) per inch and are much easier to read because of their

blue colour. Where a spirit level must also be usable upside-down, the banana-

shaped tube is replaced by a barrel-shaped tube. The upper internal surface of the

tube is thus always of the appropriate shape.

A spirit level

7.8 Plumb-bob

A plumb-bob or a plummet is a weight, usually with a pointed tip on the bottom, that

is suspended from a string and used as a vertical reference line, or plumb-line.

A plumb-bob

The instrument has been used since the time of the ancient Egyptians by

bricklayers, masons, and carpenters to ensure that their constructions are "plumb",

or perfectly upright. It may also be used in surveying to sight a point on the ground

that is not readily visible. Small plumb bobs are included in the kits of various

instruments such as levels and theodolites. They are used to set the instrument

exactly over a fixed datum marker, prior to taking fresh readings.[citation needed]

Plumb-bobs and chalk lines are often sold as a single tool.

7.9 Use

Up until the modern age, on most tall structures, plumb-bobs were used to provide

vertical datum lines for the building measurements. A section of the scaffolding

would hold a plumb line that was centered over a datum mark on the floor. As the

building proceeded upwards the plumb line would also be taken higher, still

centered on the datum. Many cathedral spires, domes and towers still have brass

datum marks inlaid into their floors, that signify the center of the structure above.

Plumb-bob with scale as an inclinometer

Although a plumb-bob and line alone can only determine a vertical, if mounted on a

suitable scale the instrument may also be used as an inclinometer to measure angles

to the vertical.

The early skyscrapers used heavy plumb-bobs hung on wire in their lift wells. The

weight would hang in a container of oil to dampen any swinging movement,

functioning as a shock absorber.

7.10 Determining centre of gravity of an irregular shape

Students of figure drawing will also make use of a plumb line to find the vertical axis

through the center of gravity of their subject and lay it down on paper as a point of

reference. The device used may be purpose-made plumb lines, or simply makeshift

devices made from a piece of string and a weighted object, such as a metal washer.

This plumb line is important for lining up anatomical geometries and visualizing the

subject's center of balance.

8. PLOTTING CONTOURS

Contours are lines that join points of equal value, in topographic surveying contours

represent points of equal height. It is difficult to observe contours directly in the

field, generally they are derived from field observations. There are two methods for

acquiring survey data for the production of contours, one using predetermined

gridded data points and the other using non-uniformly spaced data points. There

are various benefits and shortcomings with both methods.

8.1 Gridded Data Points

The points where height observations are taken are predetermined and their

locations are marked on the ground using an appropriate survey technique. This

then defines a group of rectangular prisms (see diagram) that have known

horizontal side dimensions (and a known plan area for use in volume computations,

see later).

The sides of the prisms travel over the surface of the ground between points of a

certain reduced level, and are assumed to change linearly between the corners of

the prisms. Somewhere between two points at the corners of a prism will be a point

on the line that has a value corresponding to the required contour value, generally a

whole metre or regular fractions thereof. The location of this point is then

determined by interpolating along the side of the prism.

In each of the interpolations the grid unit is known so the computations are simple

and readily automated. This is the only benefit of using gridded data, there are

however serious shortcomings.

The establishment of the grid in the field is tedious and time consuming, but more

importantly the location of the grid points is independent of the topography. The

grid ignores changes in grade, ridge lines or creek banks, and is not an accurate

method of describing the terrain. It is not recommended for use as a topographic

survey method, especially as the advent of computer reduction and plotting

packages has eliminated the hand computations.

8.2 Non-Uniformly Spaced Data Points

The field method of using non-uniformly spaced data points allows the topography

to be accurately represented. Observations are usually made to actual topographic

features such as changes in grade, tops and toes of banks or batter slopes, distinct

boundaries and so on. This is easily performed in the field using tacheometric

survey techniques, there is no need to establish points on a predetermined pattern.

While this is the most accurate representation of the terrain, the computations

involved are greatly increased in volume. The same interpolations are performed as

with gridded data (the mathematics are exactly the same) but now for each pair of

points the horizontal distance between them must be calculated or measured off the

plan. Computer packages make this very easy, but if the computations are being

performed by hand then the amount of work is substantial.

These sets of data points are known as TINs (Triangulated Irregular Networks) and

Digital Terrain Models. Examples of these are found in the notes on Volumes.