1. FFS 102 FOREST SURVEYING AND ENGINEERING (1+2)
Theory
Introduction - Principles of surveying - Errors in surveying - Scope of surveying in
forestry - Scales - Definition - Construction of Scales: simple, diagonal, vernier and
comparative scales - choice of scales - Measurement of distances - linear measurement -
chains - testing and adjusting of chains - arrows, pegs - tapes - ranging rods - ranging
out Survey lines - chaining on plain and sloping lands - errors in chaining - chaining
around obstacles - chain surveying - Principles - methods of Surveying - base, tie and
check lines - Survey with straight and irregular boundaries - offsets - methods of
recording and plotting.
Measurement of angles - objects - triangulation - instruments for measurement
of angles - compass - bearings - whole circle and reduced bearings - meridians - true,
magnetic and arbitrary meridians, local attraction - correction.
Chain and compass surveying - methods of surveying - radiation, intersection
and traversing - closed and open traverse - method of plotting - parallel meridian -
forestry field problems - laying out a coupe and its demarcation - finding horizontal
distance to an inaccessible point.
Theodolite surveying - Measurement of horizontal, vertical angles - use in
forestry - Plane table surveying - Principles - Instruments - centering and orientation -
methods of plane table surveying - Applicability in forestry.
Leveling - topographical surveying - utility and scope - leveling instruments -
dumpy level - temporary and permanent adjustments - difference in levels - bench
Marks - reduction of levels - rise and fall method - Height of collimation method.
Topographical surveying - methods of contouring - characteristics and use of
contours - Ghat tracers - principles - use - map and map reading - principles of map
reading - copying, enlargement and reduction of maps - computation of areas - methods
of computation.
Land development - material used for construction – brick, cement. Lime –
manufacturing – Masonry – brick and stone – its classification – Foundation – types and
suitability for different locations.
Roads - profile - types - classification – types of gradient – alignment of roads in
plains and hills - Bridges and Culverts – types.
Practical
Construction of scales - chain survey of an area, field work - plotting - chain and
compass surveying - Methods – Radiation, Intersection and traversing - Plane table
surveying - Radiation, Intersection and traversing. Leveling - Reduced levels -
measurement - contouring – plotting, map reading, enlargement and reduction of maps
1
2. - computation of areas. Theodolite surveying, Ghat tracer Manufacturing of brick, lime in
kilns – cement manufacturing – foundation – masonry – brick and stone. Roads -
alignment of roads in hills and plains – earthwork estimation in roads – bridges and
culverts.
Lecture Schedule
1. Introduction and principles of surveying.
2. Scales - Simple, diagonal and vernier scales
3. Measurement of distances - chains, errors in chaining, Ranging
4. Chaining on plains, slopes, around obstacles and irregular areas
5. Offset - method of plotting
6. Measurement of angles, bearings, meridian and local attraction.
7. Compass - Prismatic compass – Radiation, intersection and traversing
8. Theodolite surveying
9. Mid-Semester Examination
10. Plane table survey
11. Leveling, benchmark, reduction of levels
12. Contour - map reading - computation of areas of irregular boundaries
13. Study of minor survey instruments - Abney level, Ghat tracer
14. Materials for construction - Bricks, lime, cement
15. Foundation - types - Factors affecting foundation
16. Masonry - Brick and stone, Bonds - types
17. Road - classification - WBM and Earthen road - Bridges, culverts - types.
Practical Schedule
1) Construction of scales
2) Chaining on plain areas
3) Chaining around obstacles and irregular areas
4) Ranging of straight lines
5) Cross staff survey
6) Compass survey - Radiation
7) Compass Survey - Intersection
8) Compass Survey - Traversing
9) Plane table survey - Radiation method
10) Plane table survey - Intersection method
11) Plane table survey - Traversing
12) Demarcation of a coupe
13) Leveling using Dumpy level
14) Leveling by rise and fall method
15) Leveling by height of collimation method
16) Leveling along the forest roads using ghat Tracer
17) Profiling of forest streams by leveling
18) Contouring - field work
19) Plotting
20) Interpolation of contours
21) Map reading
2
3. 22) Computation of areas
23) Theodolite survey - measuring distances
24) Measuring angles - Height and elevation
25) Application problems on surveying
26) Visit to quarrying site
27) Study of brick and lime kilns
28) Study of different types of brick and stone masonry
29) Designing foundation for different locations
30) Alignment and setting of roads
31) Earthwork estimation of road
32) Visit to road laying sites
33) Visit to different bridges and culvert sites and recording the construction features
34) Final Practical Examination
Assignment
1. Preparation of road map of FC&RI, MTP
2. Prepare an estimate for earthwork excavation of trench around the campus
3. Preparation of contour map of FC&RI fields
Reference Books
Kanetkar,T.P. and Kulkarni, S.V. 1982. Surveying and levelling, Part I, A.V. Sathya Gruga
Prakashan, Poona - 4
Masani, N.J. 1990. Forest Engineering without Tears, Nataraj Publication, Dehra Dun.
Michael, A.M and Ohja, T.P. 1995 Principles of Agricultural Engineering - Vol.II, Jain
Brothers, New Delhi.
Negi, S.S. 1994. Hand book of Forest Engineering, International Book Distributors,
Dehra Dun.
Ram Prakash, 1983. Forest Surveying, International Book Distributors, DehraDun.
Rangawala, S.C and Rangwala, P.S. 1985. Surveying and Leveling, Character Publishing
House, Anand.
3
4. FFS102 – Forest Survey and Engineering (1+2)
Course Teacher – Dr S.V. Kottiswaran
Professor (SWC)
I. Scales
General
The distances measured on ground are plotted on paper in such a way that a fixed
ratio is maintained between the distance on ground to the corresponding distance on
paper. This ratio is known as scale and the process of plotting with scale is known as
drawing to scale. Thus, the scale is defined as the ratio of ground distance to the plotted
distance on plan, i.e.,
Scale = Ground distance
Plan distance
For instance, if the scale is 1 cm = 5 cm, it means that one cm on paper indicates five
meters on ground.
Scales can be expressed in the following three ways:
(1) Engineer's scale: In this case, the relation between the distance on plan and the
distance on ground is mentioned numerically in the style as 1 cm = 5 m, etc. such an
expression grants convenience in reading and plotting.
(2) Graphical scale: The scale is drawn on plant itself. Hence, a graphical scale
represents a line, which is subdivided into plan distance to the corresponding
convenient units of length on the ground. As the plan or map becomes old, the
engineer's scale may shrink and may not give accurate results. However, such is not
the case with graphical scale because if the plan or map shrinks, the scale will also
shrink. Hence, graphical scale is drawn on survey maps.
(3) Representative fraction: In this case, the ratio is worked out in such a way that
numerator is unity and denominator is a fraction in the same unit of measurement as
4
5. the numerator. This fraction is known as representative fraction and it is briefly
written as R.F. it is desirable to write the scale in R.F. also. For instance, R.F. of a
scale 1 cm = 5 m can be worked out as follows:
5
6. Classification of scales:
Scales are classified in the following four categories:
I. Plain scale
II. Diagonal scale
III. Vernier scale
I. Plain scale :
From this type of scale, it is possible to read only in two dimensions on paper
such as metres and decameters, hundreds and tenths, units and tenths, etc.
Solution
The procedure for construction of this scale will be as follows:
(1) Select suitable number of metres divisible by 10 and work out the
length of scale
(2) Draw a line 8 cm long the divide it into 4 equal parts. Each part then
represents 109 m.
(3) Divide the first compartment into 10 equal parts, each part
representing 1 m.
(4) Finish up the scale, and mark on it 37 m as required.
II. Diagonal scale:
From this type of scale, it is possible to read in three dimensions on paper such as
metres, decameters and centimeters; units, tenths and hundredths; etc.
Solution:
The procedure for construction of this scale will be as follows:
(1) Construct the plain scale as before.
(2) Make the construction on subdivision portion. Finish upon the scale
and mark on it 26.6 m and 30.3m.
III. Vernier scale:
To read the fractional part of the smallest division of the main or primary scale, a
device was found out by A.N. Vernier in 1631 and after his name, the device has come
to be known as vernier scale.
6
7. The difference between the smallest division on the main scale and that on the
vernier scale indicates the fineness of vernier reading and it is known as the least count of
the vernier.
Vernier scale are of the following five types:
(1) Direct vernier
(2) Retrograde vernier
(3) Extended vernier
(4) Double vernier
(5) Double-folded vernier
(1) Direct vernier:
In case of direct vernier, both the scales, namely, vernier and main move in the same
direction and they are graduated in the same direction. As shown in fig. (n-1) parts of the
main scale are taken and they are divided into n equal parts on the vernier scale.
n
Main Scale Vernier Scale
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9
(n-1)
Let d = value of the smallest division on main scale
U = value of the smallest division on vernier scale.
Then,
or
n −1
u= d
n
7
8. (n −1)d = nu
Least count of vernier = d -u
n −1
=d− d
n
n − n +1
= d
n
d
=
n
thus, the ratio of the value of the smallest division on main scale to the total number of
divisions on vernier scale indicates the least count of the vernier scale.
(2) Retrograde vernier:
In case of retrograde vernier, main scale and vernier scale move in opposite
directions and graduations are also marked in opposite directions. (n+1) parts of the main
scale are taken and they are divided I to n equal parts on the vernier scale. Thus, in case
of retrograde vernier, the divisions of vernier scale will be larger than those of main scale
and it will facilitate in easy reading. However, direct vernier is commonly used as it is
simple is operation.
Let d = value of the smallest division on main scale
u = value of the smallest division on vernier scale
Then,
(n + 1)d = nu
or
n +1
u= d
n
8
9. Least count of vernier = u -d
=
(n + 1)d d
n
d
=
n
Thus least counts of direct and retrograde verniers are the same.
(3) Extended vernier :
This type of vernier is just similar to the direct vernier scale except that every second
division is omitted. It, the therefore, follows that in case of extended vernier scale,
(2n-1) divisions of the main scale are taken and they are divided into n equal parts.
Let d = value of the smallest division on main scale
u = value of the smallest division on vernier scale
Then
(2n −1)d = nv
or
v=
(2n − 1)d
n
Least count of vernier = 2d -u
= 2d −
(2n − 1)d
n
2n − 2n + 1
= d
n
d
=
n
9
10. (4) Double vernier:
When the main scale is running in both the directions with common zero, it
becomes easier to employ a single vernier scale with common zero, as shown in fig. 2-1.
Such cases usually occur when vertical angels are to be measured with a common
horizontal plane. Extreme care should be exercised to properly read the vernier scale,
i.e., the directions of reading of main and vernier scales should be the same.
Exercise I
1. Draw a plain scale 1cm = 5m and show on it 48m.
2. Draw a diagonal scale 1cm = 4m to show m and dm. Show on the scale 23.2m and
37.4m.
3. Construct a vernier scale with least count as 1/100. The smallest division on the main
scale is 0.10m. Show a reading of 3.46m.
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11. II. Chain Surveying
Principle of chain survey
The main principle of chain survey is to prepare a framework or network of
triangles because a triangle is a figure, which can be plotted on paper by measuring its
sides only. Great care has to be exercised in the formation of well-proportioned or well-
conditioned triangles so that the process of chain surveying becomes smooth. A well-
proportioned or well-shaped triangle has no angle greater than 1200 or smaller than 300.
As far as possible, the triangles formed should resemble to the shape of an equilateral
triangle. If, however, the conditions are not favorable for forming well-proportioned
triangles, extreme care should be taken in chaining and plotting of the unavoidable ill-
proportioned or ill-conditioned triangles.
Instruments required in chain survey:
Following instruments are required for carrying out a chain surveying:
(1) Chain and 10 arrows
(2) Tape of 10 m or 20 m length
(3) Ranging rods about 10 to 15 in number
(4) Offset rod
(5) Cross-staff or optical square to set right angles
(6) Plumb bob
(7) Field book with pencils, rubber, pen-knife, etc.
(8) Box sextant, if any angle other than 900 is to be set up or measured.
(9) Miscellaneous items such as hammer, axe, nails pegs, bundle of string, chalk,
etc.
Procedure for carrying out chain survey:
Following are the four distinct steps involved in carrying out the chain survey of any plot
of land:
(1) Reconnaissance survey
(2) Marking of stations
(3) Preparation of reference sketches
(4) Running of survey lines
11
12. (1) Reconnaissance survey;
A reconnaissance survey indicates the preliminary inspection of the site of work and
hence, first of all, the survey our visits the area to be surveyed. The salient features of the
site are studied with reference to the following aspects:
(i) Index plan: The survey our prepares an index plan or sketch in the field book
showing roughly the area to e surveyed and important objects such as
buildings, roads, streams, etc. are included in this index plan. It also contains
the sequence in which the survey lines are to be measured. The stations are
indicated by number or letter and the direction in which the work is to
proceed is shown by arrows.
(ii) Main station: Suitable positions of main stations are decided by the surveyor.
The important fact to be kept in mind is the intervisibility of main stations.
The lengths of main survey lines are measured roughly by pacing or some
such approximate method of measurement.
(iii) Study of area: During reconnaissance survey, the surveyor has to carry out
intensive study of the site so that he can get a clear picture of the area to be
surveyed, probable difficulties to be encountered during the work, time
required to finish up the job, etc.
(2) Marking of stations:
The stations selected during reconnaissance survey should be properly marked on
ground by using suitable equipment so that they can be readily and easily identified.
Depending upon the nature of ground and importance of stations, the marking of stations
is done with ranging rods, wooden pegs, nails, stones, etc.
(3) Preparation of reference sketches:
After marking of stations, the location or reference sketches of these stations should
be neatly drawn in the field book. The reference sketch of a station helps in locating
the station at a future date or in cases where its position is not traceable ad it is to be
fixed again. Two measurements from permanent structures will be sufficient. But
usually three measurements are taken to ensure the check on exact location of the
stations. The measurements are taken with reference to the permanent objects that
12
13. may be in the form of corner of a building, electric or telegraph post, compound wall
or gate, trees, etc. The measurements are taken to the nearest 5-mm. North line
should invariable be drawn on the reference sketch. Thus, the position of a station is
resorted with the help of its reference sketch by swinging arcs from the respective
permanent structures.
(4) Running of survey line:
The work of chaining is then started. Base line is first to be measured. The work is
carried out as follows:
(i) Chain is laid down on the ground after proper ranging.
(ii) Offsets of nearby details are taken and recorded in the field book in the usual
manner.
(iii) Chain is then stretched or taken forward and the process is repeated till the
end of line is reached.
(iv) Other lines of the framework are then gradually taken and measured.
Plotting work
The details entered in the field book are ten plotted on paper in the drawing office.
The drawing materials required for plotting work include brushes, colours, ink,
pencils, pins, rubber, saucers, weights, etc. following are the drawing instruments
required for plotting work.
(1) compass box
(2) drawing board of suitable dimensions;
(3) drawing table;
(4) paper;
(5) protractor;
(6) rolling parallel ruler
(7) set of French curves
(8) set of scales;
(9) set squares;
(10) straight edge of steel
(11) tee - square etc.
13
14. The plotting work should be carried out carefully so that a decent well-looking
drawing emerges after the work is completed. The items such as lettering, inking,
colouring, etc. should be done in an artistic way. The map must contain the scale with
which it is drawn and the north line should be exhibited at suitable spot on the map. The
conventional signs which are commonly used must be used.
Exercise II
1. Calculate the distance of the road around the buildings of the campus by chain
surveying
2. Find the area of the field by cross staff survey
14
15. II. Compass survey
The process of triangulation is not possible when the area is to be surveyed is
large with irregular boundaries and many obstacles. In such cases, traversing is adopted.
In the process of traversing, the direction of the survey line is fixed by taking the angular
measurements with suitable instruments. Thus, a traverse consists of a series of connected
lines whose lengths and direction are known.
Compass:
The instruments which is used for finding out the magnetic bearings or simply
bearings of a line is known s a compass and any compass essentially consists of the
following three parts:
(1) Circle - with graduations;
(2) Line of sight; and
(3) Magnetic needle supported loosely.
Following are the main five types of compasses:
(1) Prismatic compass
(2) Surveyor's compass
(3) Compass over a level
(4) Trough compass
(5) Tubular compass.
Each type of the above compass will be now briefly described.
Prismatic compass:
The prismatic compass is the most convenient, handy and portable instrument. It
is circular is shape and its diameter varies from 85 mm to 110 mm. it is made up of a
non-magnetic metal. It essentially consists of the following parts;
(i) A magnetic needle of broad type supported over a centrally situated pivot
made of hard steel is provided.
(ii) A graduated aluminum ring is attached with the needle and it is divided
into degrees and half degrees. The graduations start from zero marked at
south end of the needle and they run clockwise so that 900, 1800 and 2700
15
16. are marked respectively at west, north and east. The figures are written
inverted.
(iii) Eye vane and object vane are fixed diametrically opposite to each other.
The reflecting prism is provided near eye vane. The line joining eye vane
and object vane passes through the centre of compass.
(iv) Focussing stud is provided to adjust the eyesight's of the different persons.
(v) A break pin is provided to stop the oscillations of the ring.
(vi) A glass cover is provided at the top so that dust particles cannot enter the
compass box.
(vii) Sunglasses are provided to facilitate the sighting of objects in sunlight.
(viii) A hinged mirror with sighting or object vane is provided. The mirror can
be inclined at any angle so that it becomes possible to sight the objects
which are too low or too high.
Method of using the prismatic compass:
Suppose it is required to observe the bearing of line AB. The procedure will be as
follows.
(i) The temporary adjustments of the compass are carried out. it involves two
operation, namely, centering and leveling. The process of obtaining centre
of compass over the centre of the peg is known as centering. The can be
done either by a plumb bob or by allowing a small pebble to fall from the
centre of the compass and hit the peg. The compass can be held in hand,
but it is generally mounted on a light tripod. The process of making the
needle horizontal is known as leveling and it is achieved h means of a ball
and socket joint. When the compass is leveled, the need swings freely. It
should be clamped, when perfectly leveled.
(ii) After centering and leveling of the compass is done over the station A, the
sighting vane and prism of the compass are raised. The prism is adjusted
so that readings can be clearly seen.
16
17. (iii) The compass box is rotated until the ranging rod at station B, hair of object
vane and slit of eye vane are in the same line.
(iv) The needle is brought to rest by pressing the knob, if necessary and then,
the reading is taken. The readings are usually taken upto an accuracy of
15 minutes. The reading will indicate the angle, which the line AB makes
with the north line.
Exercise III a
1. Estimate the area of the field by compass survey by radiation and traversing.
2. Find the included angles of the marked points in the field.
17
18. Measurements of angles and bearings
Definitions:
Bearings:
A bearing of a line is defined as the angle made by the line with some reference
direction or meridian.
Meridians:
Following are the three meridians that are commonly used in survey work:
(1) Arbitrary meridian
(2) Magnetic meridian
(3) True meridian.
Methods of designation:
Following are the two systems of designation of bearings;
(1) Quadrantal bearing system
(2) Whole circle bearing system
(1) Quadrantal bearing system:
In this system, the angle is measured from north or south to east or west. Thus, there
are four quadrants, namely, NE, SE, SW and NW, as shown in fig. 7-10. Thus, 9in
this system, the numerical value of the angle does not exceed 900 and it also helps in
trigonometrical calculations. The quadrantal bearings are also referred to as reduced
bearings or R.B
(2) Whole circle bearing system:
In this system, the angle is measured from the magnetic north in clockwise direction
and its value will therefore vary from 00 to 3600. The bearing is known as whole
circle bearing or W.C.B.
Every line has two bearings, namely, fore bearing (F.B) and back bearing (B.B.). The
reading of line AB taken from point a is the F.B. of line AB and the reading of line AB
taken from point B is its B.B.
18
19. Let us consider the W.C.B. system for finding out the relation between F.B. and
B.B. of a given line AB.
In case I,
B.B. = F.B. + 1800
In case II ,
B.B. = F.B. - 1800.
Thus, a general expression can be framed as follows:
B.B. = F.B. ± 1800.
Use + sign if F.B. is less than 1800 and
Use - sign if F.B. is greater than 1800.
In the quadrantal system, there will not be any changes in the value of F.B. and
B.B. except that their respective quadrants will be interchanged. Thus if F.B. is in NE
quadrant, B.B. will be in SW quadrant. Thus N is to be substituted for S and E is to be
substituted for W and so on.
Exercise III b
1. Convert the Q.B. to W.C.B.
a. N120 280 E. b. N 680 270 W c. S 430 380 E d. S 370 520 W
2. Convert W.C.B. to Q.B.
a. 3050 170' b. 650 40' c. 1710 37' d. 2080 19'
19
20. IV Plane Table Survey
General
In case of plane table survey, the measurements of survey lines of the traverse and
their plotting to a suitable scale are done simultaneously on the field. Following are the
cases in which the plane table survey is found to be useful.
(1) Compass survey cannot be carried out with success in industrial areas of the
town. Plane table survey will be the best alternative in such cases.
(2) For preparing plans on a small scale, plane table survey proves to be speedy,
easy and accurate.
(3) The city or town has expanded within two or three decades and it is required
to plot the developed area on the previously plotted plan of the existing area.
Instruments required for plane table survey:
(1) Alidade
(2) Drawing board.
Accessories required for plane table survey:
(1) Plumbing fork
(2) Spirit level
(3) Trough compass
(4) Miscellaneous.
Miscellaneous:
In addition to the above-mentioned accessories, the miscellaneous items required
will be the drawing paper of the best quality, pencil, rubber, scale, pins, water-proof
cover to protect the board, etc.
20
21. Temporary adjustments of plane table:
Following three distinct operations at each survey station are carried out for the
temporary adjustments of a plane table;
(1) Centering
(2) Levelling
(3) Orientation.
Methods of plane table survey
Following re the four methods by which an object might be located on paper by
plane table:
(1) Radiation
(2) Intersection
(3) Traversing
(4) Resection.
(1) Radiation:
This is the simplest method and it is useful only when the whole traverse can be
commanded from a single station. The procedure is as follows:
(2) Intersection:
This method is useful where it is not possible to measure the distances on ground as
in case of a mountainous country. Hence, this method is employed for locating
inaccessible points, the broken boundaries, rivers, fixing survey stations, etc.
21
22. (3) Traversing:
This method resembles the work of a compass survey and it is useful for the survey
work of roads, rivers, etc. the traverse is run as usual and the details on the line are
taken by radiation or offsets.
(4) Resection:
The process of resection is used for establishing the instrument stations only and it
thus helps in ascertaining the fact that the point plotted on plan is the station occupied
by the plane table.
Exercise IV
1. By plane table survey using radiation method and intersection method plot the field
boundaries.
2. Find the area of the field by triangulation.
22
23. V Levelling
General
Levelling is defined as a method of determining the relative elevations of points
on the surface of earth or an operation for finding out the difference in heights. Thus, the
data obtained from the process of Levelling will be useful in the following two respects;
(1) To establish points for various engineering purposes at desired elevations
with respect to a given datum.
(2) To work out the elevations of given points relative to each other or with
respect to a given datum.
Definitions of some common terms in levellings:
(1) Backsight and foresight and intermediate sight: Backsight or B.S. is the first
reading from any set up of the instrument and foresight or F.S. is the last
reading taken before disturbing the instrument from its set up. All sights
taken between B.S. and F.S. are known as intermediate sights or I.S.
(2) Bench mark: A fixed point of known elevation is called the bench mark or
B.M.
(3) Change point or turning point: The point indicating the shifting of level is
known as a change point (C.P.) or a turning point (T.P.)
(4) Datum: A datum surface or line is any arbitrarily assumed level surface or
line from which the vertical distance are measured.
(5) Elevation: The vertical distance of a point with respect to a given datum,
either positive or negative, is known as the elevation of that point.
(6) Height of instrument: The elevation or R.L. of the line of collimation, when
the instrument is correctly levelled, is known as the height of instrument.
23
24. (7) Horizontal line: The line in a horizontal plane is known as a horizontal line.
A horizontal plane at any point is a plane tangential to the level surface at that
point
(8) Level line: The line drawn on a level surface is known as a level line.
(9) Level surface: This is a surface on which all the points are equidistant from
the centre of earth. As earth is sphere, a level surface will be a curved
surface. Examples of a level surface are liquid surface or a sea water, liquid
surface of lake, etc.
(10) Line of collimation: The line joining the intersection of cross-hairs and
optical centre of the object glass and its continuation is known as line of
collimation.
(11) Mean sea level: The average height of the sea for all states of the tides is
known as mean sea level or M.S.L.
(12) Reduced level: The elevation of a point or its vertical distance above or
below the datum is known as its reduced level or R.L.
(13) Station: The point which is to be set up at a given elevation or whose
elevation is to be found out is known as the station and it thus indicates the
point at which the staff is held and not the point at which the level is set up.
(14) Vertical angle: The angle formed by the intersection of two lines in a
vertical plane is known as the vertical angle.
(15) Vertical line or plumb line: The line normal to a level surface is known as
a vertical line or a plumb line and the plane which contains a vertical line is
called a vertical plane.
24
25. Principles of levelling
Some of the important principles that are to be observed in simple direct levelling
are as follows.
(1) Change point: The intermediate staff should be carefully selected and it
should be in the form of firm point which can be easily located. The
elevation of change point should be carefully determined as a slight error in
it will be reflected in the subsequent readings. If convenient, a bench mark
can be used as a change point.
(2) Lengths of B.S. and F.S.: For accurate work, the lengths of B.S. and F.S.
should be maintained nearly equal. If this condition is satisfied, the error due
to non-parallelism of the line of collimation and the bubble line will be
reduced to a great extent. This fact can be proved by considering the line of
collimation downwards and upwards.
Entering the staff readings:
The staff readings are to be noted immediately after they are observed. For this
purpose, a level book with specially ruled out columns is used. Following points should
be observed at the time of entering staff readings in a field book:
(1) The staff readings should be entered in proper columns and in order of their
observations.
(2) The first entry and the last entry on any page are respectively B.S. and F.S.
Hence, if I.S. is to be carried over to the next page, it is to be entered as I.S.
and F.S. on the carried forward page and B.S. and I.S. on the brought forward
page.
(3) For each staff reading, a horizontal row is reserved except for staff reading of
a C.P. In case of staff reading for a C.P., F.S. of C.P. are written in the same
25
26. horizontal line with the note of C.P. in the remarks column in the same
horizontal line.
(4) The R.L. of plane of collimation should be written in line with B.S.
(5) The description of B.M. should be briefly and accurately written in the
remarks column. If required, the description of other important, features and
change points may be entered in the remarks column and the sketches may be
drawn on the left hand side of the page.
Reduction of levels:
Following are the two methods of working out the reduced levels of points from
the observed staff readings:
(1) Collimation system
(2) Rise and fall system
(1) Collimation system;
In this system, the level of line of collimation is found out by adding the B.S. taken
on B.M. of known R.L. the readings of various other points, when subtracted from this
level, will give the R.L. of the respective points. At every point, a new level of line of
collimation is obtained and the process is repeated till the last point is reached.
The arithmetical check of this system is carried out by applying the following rule:
∑ F.S. - ∑ B.S. = First R.L. - Last R.L.
It should, however, be noted that the above rule does not provide the check on the
reduced levels of the intermediate points. However, this system proves to be easy,
simple and rapid.
26
27. (2) Rise and fall system:
This system consists of finding out the difference in levels between two consecutive
points by comparing each point with the preceding point. Rise is indicated, if the staff
reading is smaller and fall is indicated, if the staff reading is greater. By adding rise or
subtracting the fall, R.L. of each point can be obtained
This system provides arithmetical checks in three ways as follows:
∑ F.S. - ∑ B.S. = Σ Falls - ∑ Rises = First R.L. - Last R.L.
It is thus seen that this system provides a complete check on intermediate calculations
also. Hence, this system, though laborious and tedious, is adopted for accurate work.
Exercise V
1. Find the reduced levels of the points of the given points by height of collimation
method and rise and fall method and check arithmetically
27
28. VI Contouring
General:
A contour is an imaginary line, which joins the points of equal elevation on the
ground. Thus, it represents a line in which the surface of the ground is intersected by a
level surface. The plan showing the elevations and depressions of the surface of the
ground is known as the contour plan or contour map.
Contour interval:
The vertical distance between any two consecutive contours in known as contour
interval and it is kept constant for a contour plane, once it is adopted. The horizontal
distance between two points on two consecutive contours is known as the horizontal
equivalent and it will naturally depend on the steepness of the ground
Interpolation of contours:
The process of placing or spacing the contour lines proportionally between the
plotted ground points is known as the interpolation of contours and it is based on the
assumption that the slope of ground between the two point is uniforms. Following are the
three methods of interpolation of contours:
(1) Estimation
(2) Arithmetical calculations
(3) Graphical.
(1) Estimation;
In this method, the position of contour point is judged by estimation only. The
method is rapid. But as it give approximate results, it is useful for small scale maps
only.
28
29. (2) arithmetical calculations;
In this method, the position of contour point is worked out by exact mathematical
calculation. Let us take a simple case to illustrate this method. IF two-ground points
P and Q are situated at a distance of 25 m with respective elevations as 80.50 m and
70.50 m. Assuming, the contour intervals as 2 m, the contour points for 72 m, 74 m,
76 m, 78 m and 80 m will have to be established on line PQ by applying the rule of
three.
Now, difference in levels between P and Q = 80.50-70.50
= 10 m.
Distance between P and Q = 25 m.
25 x0.5
= = 1.25m
10
Similarly, distance of 78 m contour point from P
25 x 2.5
= = 6.25m
10
distance of 76 m contour point from P
25 x 4.5
= = 11.25m
10
Exercise VI
1. Find the reduced levels of the points in the field for a given grid interval and plot the
contour map of the area.
29
30. VII. Computation of Areas
Methods for computation of areas
Following are three methods adopted for the purpose of computing the areas:
I. Geometrical figures
II. Ordinates
III. Planimeter
II. Ordinates
The above method becomes tedious especially when the plot is in the form of a
long narrow strip and hence, in such cases, the area of the plot is computed by drawing a
base line and ordinates are put up along this base line at regular intervals. The height of
each ordinate is measured. By knowing the length of constant interval between the
ordinates and height of each ordinate, the area of the plot can be computed by adopting
any one of the following rules:
1. Mid-ordinate rule
2. Average ordinate rule
3. Trapezoidal or average end area rule
4. Simpson or parabolic rule
(1) Mid –ordinate rule
Let n = Number of equal parts
d= Length of each equal part
L= Length of base line = nd or d= L/n
30
31. h1, h2 etc = Ordinates at mid-points of each division.
Then,
Area = dh1+dh2+dh3+ . . .. dhn
= d(h1+h2+h3+ . . . . hn )
= L/n (h1+h2+h3+ . . .. hn)
(2) Average ordinate rule
In this case, the length of average ordinate is obtained by dividing the sum of all
ordinates with the total number of ordinates measured.
Let O1, O2, etc. = Ordinates at each of the points of division n,d and L as above.
Then
Number of ordinates = n+1
O0 + O1 + O2 .... + On
Area =
n +1
(3) Trapezoidal or average end area rule:
In this case, the area of each trapezium formed between successive divisions is
calculated independently and then added together to obtain the total area of the plot. This
method of more accurate than the previous two methods.
O + O1 O + O2 O + On
= 0 d+ 1 d + ....... n −1 d
2 2 2
31
32. = d 2[O0 + 2O1 + 2O2 + 2O3 + ....... + On ]
O + On
= d 0 + O1 + O2 + O3 + ........ + On −1
2
(4) Simpson or parabolic rule
In this case, the boundary of the plot is not assumed straight. But it is considered
as a curve in the form of a parabola.
Area of figure ABGDE = area of trapezium ABGE + area under curve EDG
O + O2
= 0 x 2d + 2 × Area of parallelogram CFGE
2 3
O + O2
= 0 x 2d + 2 × 2d × DH
2 3
O0 + O2
Now DH = O1 −
2
O + O2 O + O2
= 0 x 2d + 2 × 2d × O1 − 0
2 3 2
= d/3 [3Oo+3O2+4O1 - 2O0 - 2O2]
= d/3 [ Oo+4O1+O2]
Similarly, area between ordinates O2 and O4 will be given by the equation.
32
33. = d/3 [ O2+4O3+O4] and so on.
Hence, total area between ordinates Oo and O4= d/3 [ Oo+4O1+2O2 + 4O3 + O4]
The above rule can be summarized as follows: d/3 [ Oo+4O1+2O2 + 4O3 +. . . . . .
2On-2+4On-1 + On]
It is thus seen that there should be even number of divisions of the area or in other words,
the total number of ordinates must be odd. If this is not the case, the area of the last
division is worked out separately and then, added together to obtain the final area. The
area of plot, if worked out by this rule, gives better results as compared o above
mentioned all the rules.
Exercise VII
1. Following perpendicular offsets were taken from a chain line to a curved boundary line
at intervals of 10m:
0,7.38, 5.26, 6.45, 7.33, 7.87, 8.23, 0.
Compute the area between the chain line, the curved boundary line and the end
offsets by applying (1) average ordinate rule, (2) trapezoidal rule, and (3) simpson
rule.
2. Following table gives the perpendicular offsets taken from the center-line of road to a
hedge:
Offset no. Oo O1 O2 O3 O4 O5 O6 O7 O8
Offset in m 4 6 5 7 5 4 3 4 6
Distance in m 0 15 30 45 60 80 100 110 120
Compute he area between the center-line of road and hedge by applying (1) trapezoidal
rule and (2) Simpson rule.
33
34. VIII. Theodolite Surveying
General
The Theodolite is an extraordinary accurate instrument used in surveying for
measuring horizontal and vertical angles. It has also very wide applications in various
surveying operations such as establishing grades, setting out curves, extending survey
lines, etc. Thus, a Theodolite is an instrument for angular measurements and it given
angles of required precision.
Definitions and terms used for Theodolite work
It is necessary to clearly understand the meanings of the following terms that are
used during the manipulation process of a Theodolite:
(1) Axis of level tube: It is a straight line tangential to the longitudinal curve of the
level tube at its center. It is also known as the bubble line and it is horizontal,
when the bubble is central.
(2) Axis of telescope: It is the line joining the optical center of the object glass to the
center of the eyepiece.
(3) Centering: It is the operation carried out to ascertain the fact that the vertical axis
of the instrument passes through the center of the peg fixed at the required station
point. It is carried out by suspending a plumb bob from the underside of the
instrument.
(4) Changing face: The operation of changing the position of vertical circle either
from left to right or from right to left of the observer is known as changing face.
For a transit Theodolite, it is done by revolving the telescope through 180o in the
vertical plane and through 180o in a horizontal plane. For a non-transit
Theodolite, releasing and then do it, reversing the telescope for end to end.
(5) Face left: When the vertical circle of the instrument is on the left of the observer
taking reading, the position is known as face left position and in such position,
34
35. the telescope is said to be in normal or direct or in bubble up position. The
observation of an angle (horizontal or vertical) made with face left position is
known as face left (F.L) observation.
(6) Face right: When the vertical circle of the instrument is on the right of the
observer taking reading, the position is known as face right position and in such
position, the telescope is said to be in inverted or reversed or in bubble down
position. The observation of an angle (horizontal or vertical) made with face
right position is known as face right (F.R) observation.
(7) Horizontal axis: It is the axis about which the telescope and the vertical circle
rotate in a vertical plane. It is also known as trunnion axis or transverse axis.
(8) Line of sight: The term line of sight or line of collimation is used to indicate an
imaginary line joining the optical center of the object glass and intersection of the
crosshairs of the diaphragm and its continuation.
(9) Swinging the telescope: It is the operation of turning the instrument in a
horizontal plane about its vertical axis. Swinging is said to be right swing if the
instrument is moved in clockwise direction and it is said to be left swing, if the
instrument is moved in anti-clockwise direction.
(10) Transitting: It is the operation of revolving the telescope in a vertical plane by
180o about the horizontal or trunnion axis. It is also referred to as plunging or
reversing.
(11)Vertical axis: It is the axis about which the telescope can be rotated in a
horizontal plane. The lower and upper plates of the instrument rotate about this
axis.
Temporary adjustments of Theodolite
At every set up of the instrument, certain temporary operations are carried out
before the observations are made. These operations are known as temporary
adjustments or station adjustments and they are made to achieve the following two
conditions.
35
36. 1. The plane of collimation is horizontal
2. The vertical axis passes through the center of the peg.
Following are the three temporary adjustments of a Theodolite:
1. Levelling up
2. Elimination of parallax.
Measurement of horizontal angles
The general procedure for measuring horizontal angle by theodolite will be as
follows.
(1) The instrument is set up at station O and the temporary adjustments are
performed to level it accurately.
(2) Let the verniers on upper plate be named as A and B. Adjust the vernier
A to the zero (usually marked 360o) of the horizontal circle. If there is
no instrumental error, the reading on vernier B will be 180o. Also see
that the vertical circle is to the left. Now both plates are clamped and
thus the instrument will revolve about its outer axis.
(3) The lower clamp is loosened and it is pointed towards the left hand side
object P. The lower clamp is tightened and the object is bisected
accurately by using the lower tangent screw. The readings of verniers A
and B should be checked and as such, there should be not change in the
previous readings. It may also be noted that the left hand side object is
bisected first because of the fact that the graduations on the scale plate
run in clockwise direction.
36
37. (4) The upper clamp is loosened and the instrument is rotated clockwise
about the inner axis to bisect the object Q. The upper clamp is then
clamped and the object Q is bisected accurately by using upper tangent
screw.
(5) The readings of both the verniers are taken. The reading of vernier A
gives directly the angle POQ while the value of angle POQ on vernier B
can be obtained by deducting 180o from the reading.
(6) The man value of two readings gives the angle POQ with one face.
(7) The face is changed by transiting the telescope and the whole process is
repeated. Thus, mean value of angle POQ is obtained with other face.
(8) The average horizontal angle is thus obtained by taking the mean of the
two values obtained with two faces.
During the above process, care should be taken to manipulate the proper clamps and
to record the readings properly. It is also not necessary to set vernier A to zero initially.
It may be set at any desired reading. But in that case, the difference between the initial
and final readings on vernier A should be worked out to get the angle POQ.
For measuring horizontal angles with high precision without increasing the size of the
scale plate, the following two methods have been found out:
(1) Repetition method
(2) Reiteration method
(1) Repetition method
In this method, the same angle is repeatedly measured two times or more by
allowing the vernier to remain clamped each time at the end of each measurement and
thus, the angle is added several times mechanically. However, care should be taken to
add 360o for every complete evolution to the final reading. The average horizontal angle
37
38. is then obtained by dividing the final reading by the number of repetitions. The face is
then changed and the whole process is repeated. Thus, the average horizontal angle is
obtained by taking the mean of the two value obtained by taking the mean of the two
values obtained with two faces.
The procedure is the same as described above. But is is more exhaustive and
laborious. However, there is no advantage by increasing the number of repetitions
indefinitely. Usually the angle is accumulated three times with each face and it gives
fairly accurate result.
When this method is adopted, the following errors are eliminated:
(1) Error due to eccentricity of verniers;
(2) Error due to inaccurate bisection of the object;
(3) Error due to inaccurate graduations and
(4) Error due to line of collimation and trunnion axis not being perpendicular to each
other.
The repetition method of measuring horizontal angle does not eliminate errors due to slip,
displacement of station signals, dislevelment of the bubble, etc. because these errors are
cumulative in nature.
(2) Reiteration method
This method is also known as method of series or direction method. It is
generally preferred when several angles are to be measured at a station. The procedure
consists in measuring successively several angles in clockwise direction and finally the
horizon is closed. The term closing the horizon is used to mean the process of measuring
the angle between the last station and the initial station. Thus, it gives a check on the
angle measured because of the fact that sum of angles around a point is 360o. This
method is less tedious than the repetition method and it gives equally precise
observations in short time.
38
39. Measurement of vertical angles:
The angle made between the inclined line of sight and the horizontal line of
collimation is known as the vertical angle. If the point is above the horizontal plane, it is
called the angle of depression and is treated as negative.
Following is the procedure for measuring vertical angle, as shown in
(1) The instrument is set up at station O and it is leveled accurately with reference to
the altitude bubble.
(2) The zero of vertical vernier is exactly set to zero of the vertical circle with the
help of the vertical circle with the help of the vertical circle clamp and tangent
screw.
(3) The bubble of the altitude level is brought at the center by means of the clip
screws. Thus, the line of collimation becomes horizontal with respect to the zero
reading on the vernier.
(4) The vertical circle clamp is loosened and the telescope is sighted in vertical plane
to P. The accurate bisection is obtained with the help of vertical circle tangent
screw.
(5) The readings on both the verniers of vertical circle are taken, the mean of which
gives the required vertical angle.
(6) The face is changed and another value of angle is obtained by repeating the
process.
(7) The average vertical angle is thus obtained by taking the mean of the two values
obtained with two faces.
It is easy to understand that the above procedure can also be adopted to measure the
vertical angle between two points subtended at the instrument station. It will be equal
to the sum or difference of the two readings depending on the relative positions of the
points with reference to the horizontal line of collimation.
Exercise VIII
1. Determine the horizontal angles by theodolite survey
2. Using the theodolite find the vertical angle and horizontal distances
39
40. IX. Ghat tracer
Ghat tracer is an useful instrument for finding gradients, setting out grade contours,
preliminary survey of hill route for road alignment and also for contouring and
leveling.
Construction: It consists of a triangular frame with a hollow metal sighting tube fitted
with an eyepiece at one end and with cross wires at the other. It is hung by a pivot at
apex, on an upright staff, by means of a clamping pin and nut. About 2 to 3 cm below
the sighting tube and parallel to it there is a racked horizontal bar, attached to the tube
rigidly by 2 small vertical bars, one at other end. A weight suspended on the bar can
be moved along the racked bar by means of a screw, fixed on the supporting bracket,
operating the pinion on the rack. Upper part of the weight has a knife edge, which
forms an index, by which readings can be taken on the scale of the gradients of 1 in 6
or 1 in 120. The line of sight is the line joining the centre of the eyehole and the
intersection of cross wires. The tube and consequently the line of sight can be set to
any desired gradient by moving the weight of the racked bar.
Method of use:
The T shaped sight vane or target, on which readings are taken, has its cross line at
the same height as the height of the axis of the sighting tube. To find the gradient of
slope an assistant is sent ahead with the sight vane and the weight is moved along the
bar till the cross wires are aligned on the sight vane and the gradient read on the
scale. When the sight is taken uphill weight is moved backward from zero mark and
vice versa. If it is desired to layout on the ground an alignment at a fixed gradient the
index is set to the required gradient and the weight screwed down. An assistant is
sent with the sight vane, who moves up and down till he is on the required gradient.
To establish a line of sight, set the index exactly in the centre of the sighting tube at
zero gradients.
Exercise IX
1. Using the ghat tracer mark the contours of the alignment
40
41. CONTENTS
Ex. No. Title Page No.
I. Scales 1
II. Chain Surveying 7
III. Compass Surveying 11
IV. Plane Table surveying 16
V. Levelling 19
VI. Contouring 24
VII. Computation of areas 26
VIII. Theodolite surveying 30
IX. Ghat tracer 36
41
