Forest Surveying

7/30/2019 Forest Surveying

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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 onground 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 isunity and denominator is a fraction in the same unit of measurement as

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:

Classification of scales:

Scales are classified in the following fourcategories:

I. Plain scaleII. Diagonal scaleIII. Vernier scaleI. 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 ofscale


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(2) Draw a line 8 cm long the divide it into 4 equal parts. Each part thenrepresents 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.

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

Let d = value of the smallest division on main scale U =

value of the smallest division on vernier scale.

\ 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9

Main Scale Vernier Scale

(n-1


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Then, or

(n - 1)d = nu

n -1 ,u = ----- d

n


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n

fnn +1

n

dn

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

Least count of vernier = u -d = (n + 1)dd

d

Least count of vernier = d -u

n 1 = d-------------d

n


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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

(2n - 1)dv = -

n

Least count of vernier = 2d -u

= 2d -(2n - 1)d

n

d ^ 2n - 2n +1

d

n

(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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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

(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:


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(i) Index plan: The survey our prepares an index plan or sketch in the field book showingroughly 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. Theimportant 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 intensivestudy 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 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.


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(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.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 surveying2. Find the area of the field by cross staff survey

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


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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;

A magnetic needle of broad type supported over a centrally situated pivot made of

hard steel is provided.

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

are marked respectively at west, north and east. The figures are written inverted.

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.

Focussing stud is provided to adjust the eyesight's of the different persons.

A break pin is provided to stop the oscillations of the ring.


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A glass cover is provided at the top so that dust particles cannot enter the compass

box.

Sunglasses are provided to facilitate the sighting of objects in sunlight.

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 twooperation, 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 sightingvane and prism of the compass are raised. The prism is adjusted so that readings

can be clearly seen.

(iii) The compass box is rotated until the ranging rod at station B, hair of object vaneand slit of eye vane are in the same line.

(iv) The needle is brought to rest by pressing the knob, if necessary and then, thereading 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 a1. 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.


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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 90

0

and it also helps in trigonometricalcalculations. 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.

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. - 180'


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Thus, a general expression can be framed as follows:

B.B. = F.B. 180a Use +

sign if F.B. is less than 1800 and Use - sign

if F.B. is greater than 180a

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'

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 andaccurate.

(3) The city or town has expanded within two or three decades and it is required to plotthe developed area on the previously plotted plan of the existing area.

Instruments required for plane table survey:(1)Alidade


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(2)Drawing board. Accessories requiredfor 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.

Temporary adjustments of plane table:

Following three distinct operations at each survey station are carried out for the temporary

adjustments of a plane table;

Centering

Levelling

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.


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(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.

(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 fieldboundaries.

2. Find the area of the field by triangulation.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;


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(1) To establish points for various engineering purposes at desired elevations withrespect to a given datum.

(2) To work out the elevations of given points relative to each other or with respect to agiven datum.

Definitions of some common terms in levellings:

(1) Backsight and foresight and intermediate sight: Backsight or B.S. is the first readingfrom 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 fromwhich the vertical distance are measured.

(5) Elevation: The vertical distance of a point with respect to a given datum, eitherpositive 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 theinstrument is correctly levelled, is known as the height of instrument.

(7) Horizontal line: The line in a horizontal plane is known as a horizontal line. A horizontalplane 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 ofthe 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 meansea level or M.S.L.


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(12) Reduced level: The elevation of a point or its vertical distance above or below the datum isknown 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 befound 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 isknown as the vertical angle.

(15) Vertical line or plumb line: The line normal to a level surface is known as a vertical line ora plumb line and the plane which contains a vertical line is called a vertical plane.

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 inthe 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 bemaintained 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 theirobservations.


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(2)The first entry and the last entry on any page are respectively B.S. and F.S. Hence, ifI.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. Incase of staff reading for a C.P., F.S. of C.P. are written in the same

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:

I F.S. - I B.S. = First R.L. - Last R.L.


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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.

(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: I F.S.- I B.S. = L Falls - I 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

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:


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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.


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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.

^rr)=1.25m

Similarly, distance of 78 m contour point from P f

25x2.5"6.25m

10

distance of 76 m contour point from P f

25x4.5"

11.25m10

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.

(2) arithmetical calculations;


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VII. Computation of Areas

Methods for computation of areas

Following are three methods adopted for the purpose of computing the areas:

Geometrical figures

Ordinates

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 rule2.

Average ordinate rule

3. Trapezoidal or average end area rule4. 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


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Then,

Area = dh1+dh2+dh3+ . . .. dhn

= d(hx+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 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.

= { OIOl d + O L+O l d + ........... 0_, +On d 1I 2 2 2 I

Area

h1, h2 etc = Ordinates at mid-points of each division.


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= d/ 2[O0 + 2O1 + 2O2 + 2O3 + ........ + On ]

+ O1+O2+ O +................ + On-1

(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 + On'0

' x2d I + 2/ x Area of parallelogram CFGE2 J /3

Oo + O x2d] + % x 2d x DH{ 2 J /3

^ Oo + O2Now DH = O10 2

2

(O 0 + O 2 _ ^ 2 / , , Oo + O2-----1 x2dI + % x 2d x O1 -

0------ -

2 J /3 1 2

= d/3 [3Oo+3O2+4Ox - 2Oo - 2O2] = d/3 [ Oo+4Ox+Oi] Similarly, area between ordinates

O2 and O4 will be given by the equation.

d


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= d/3 [ O2+4O3+O4] and so on.

Hence, total area between ordinates Oo and O4=

The above rule can be summarized as follows:

d/3 [ Oo+4O1+2O2 + 4O3 + O4]

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 atintervals 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 ahedge:

Compute he area between the center-line of road and hedge by applying (1) trapezoidal rule

and (2) Simpson rule.

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


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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 itscenter. 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 theeyepiece.

(3) Centering: It is the operation carried out to ascertain the fact that the vertical axis of theinstrument 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 rightor 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,

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.


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(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 verticalplane. 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 joiningthe 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 itsvertical 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 180 o about thehorizontal 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.

1. The plane of collimation is horizontal2. The vertical axis passes through the center of the peg.

Following are the three temporary adjustments of a Theodolite:

1. Levelling up


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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 levelit 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 lowerclamp 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.

(4) The upper clamp is loosened and the instrument is rotated clockwise about the inneraxis 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 theangle 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 valuesobtained with two faces.


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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 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.


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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 360 o. This method is

less tedious than the repetition method and it gives equally precise observations in short time.

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 altitudebubble.

(2) The zero of vertical vernier is exactly set to zero of the vertical circle with the help of the verticalcircle 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, theline 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. Theaccurate 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 therequired 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


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1.Determine the horizontal angles by theodolite survey2.Using the theodolite find the vertical angle and horizontal distances

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


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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

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