unit-5-plane-table-survey-orientation-radiation-intersection-traversing-resection-two-three-point-problem-area-volume-calculation-2021-2 (1).pdf

Survey

1. Surveying
Prof. Rajesh Bhagat
Asst. Professor, CED, YCCE, Nagpur
B. E. (Civil Engg.) M. Tech. (Enviro. Engg.)
GCOE, Amravati VNIT, Nagpur
Experience & Achievement:
Selected Scientist, NEERI-CSIR, Govt. of India.
GATE Qualified Three Times.
UGC-NET Qualified in First Attempt.
Selected Junior Engineer, ZP Washim.
Three Times Selected as UGC Approved Assistant Professor.
Assistant Professor, PCE, Nagpur.
Assistant Professor, Cummins College of Engg. For Women, Nagpur
Topper of Pre-PhD Course Work at UGC-HRDC, RTMNU Nagpur

Mobile No.:- 8483002277 / 8483003474 Email ID :- [email protected]
Website:- www.rajeysh7bhagat.wordpress.com

2. UNIT-V
1)Plane Table Survey: Equipment’s, advantages and
disadvantages, orientation, methods of plane tabling, two point
and three point problems in plane tabling.
2)Computation of Area and Volume: Trapezoidal and Simpsons
Rule.

2

3. References:-

SN Title Authors Publisher
1
Surveying and Leveling
(Vol-I & II)
Kanitkar T. P.,
Kulkarni S. V.

Pune Vidyarthi Griha Prakashan, Pune.
2
Surveying and Leveling
(Vol–I & II)
Punmia B. C.,
Jain A. K.,
Jain A. K.
Laxmi Publication(P) Ltd. New Delhi.
3 Surveying & Leveling Basak N. N. Tata McGraw Hill Pub. Co. Ltd. New Delhi

4. Plane Table Surveying:
Plane Tabling is a graphical method of surveying in which the field work and
plotting are done simultaneously.
 Useful to fill interior details between stations fixed by triangulation or
theodolite traversing.
 Particularly adapted for small scale or medium scale mapping in which great
accuracy in detail is not required.
The plane table consists following accessories :
1.A drawing board mounted on a tripod
2.A straight edge called an alidade. (Plain & Telescopic)
3.Compass (Trough & Circular Box)
4.Plumbing Fork with Plumb Bob
5.Spirit Level

6. 6
Drawing Board:-
1)Made of well-seasoned wood such as teak or pine.
2)Size varies from 75 cm x 60 cm.
3) It is mounted on a tripod in such a manner that it can be leveled, and revolved
about a vertical axis and clamped in any position.

7. Plain Alidade:-
1)Consists of a metal (brass or gunmetal) or boxwood straight edge or ruler about 50
cm long.
2)The beveled (ruling or working) edge of the alidade is called the fiducial edge.
3)It consists of two vanes at the ends, the vanes are hinged and can be folded when the
alidade is not in use.
4)One of the sight vanes is provided with a narrow slit with three holes, one at the top,
one at the bottom and one in the middle and the other vane known as object vane, is
open and carried a hair or a fine thread or a thin wire stretched between the top and
bottom of the slit.
5)With the help of slit, a definite line of sight may be established parallel to the
ruling edge of the alidade.
6)A plain alidade can be used only when the elevations of the of the objects are low.

8. Plain Alidade :-
Sight Vane
Object Vane
Fiducial Edge

10. Telescopic Alidade
Telescopic Alidade

11. Spirit Level:-
1)It consists of a small metal tube which contains a small bubble.
2) The spirit level may also be circular but its base must be flat so that it can be laid on
the table.
3) The table is truly level when the bubble remains central all over the table.
4)Spirit level is used for ascertaining if the table is properly level.
5)Table is leveled by placing level in two position at right angles.

12. Magnetic Compass :-
A box compass consists of a magnetic needle pivoted at its centre freely.
 It is used for orienting the plane table to magnetic north.
 The edges of the box compass are straight and the bottom is perfectly flat.

13. Plumbing Fork:-
1)Plumbing fork consists of a hair pin-shaped brass frame, having two equal arms.
2) One end has a pointer while a plumb bob is attached the other end.
3) It is used in large scale survey for accurate centering of the station location on
the table over its ground position.
4)It is also used for transferring the location of the instrument station on the sheet
on to the ground.
5)The fork is placed with its upper arm lying on the top of the table and the lower
arm below it. The table is said to be centered when the plumb bob hangs freely
over ground mark.

15. Advantages of Plane Table Surveying :-
1)It is most suitable for preparing small-scale maps.
2)It is most rapid.
3)The field book is not necessary as plotting is done in the field concurrently with
the field work, and hence the mistakes in booking the field notes are avoided.
4)The surveyor can compare the plotted work with the actual features of the area
surveyed and thus can ascertain if it represents them properly.
5)It is particularly advantageous in magnetic areas where compass survey is not
reliable.
6)It is less costly than a theodolite survey.
7)No great skill is required to prepare a satisfactory map.

16. Disadvantages of Plane Table Surveying :-
1)It is not suitable for work in a wet climate.
2)It is heavy, cumbersome and awkward to carry.
3)There are several accessories to be carried, and, therefore, they are likely to be lost.
4)It is not intended for accurate work.
5)If the survey is to be re-plotted to a different scale or quantities are to be computed,
it is a great inconvenience in absence of the field notes.

17. 17
Setting up Plane Table :-
1)Fixing The Table on Tripod Stand: The table should be set up at a convenient
height. (say about 1m). The legs of the tripod should be spread well apart, and
firmly fixed into the ground. Table is fixed on it by a wing nut at the bottom.
2) Centering The Table: The table should be so placed over the station on the ground
that the point plotted on the sheet corresponding to the station occupied should be
exactly over the station on the ground. This operation is known as the centering of
the table. This may be done using a plumbing fork or U-frame.
3)Leveling The Table: The table top is made truly horizontal by spirit level. For
rough and small scale work, leveling can be done by eye estimation whereas for
accurate and large scale work, leveling achieved with an ordinary spirit level. The
leveling is specially important in hilly terrain. The dis-leveling of the plane table,
throws the location of the point considerably out of its true location.

18. Setting up Plane Table :-
4)Marking The North Line: Trough compass is placed on the right hand top corner
with its north end approximately towards the north. Then the compass is turned
clockwise or anticlockwise so that the needle coincides exactly with the 0-0 marks.
Now a line representing the north line is drawn through the edge of the compass.
5) Orientation: When plane table survey is to be conducted by connecting several
stations, the orientation must be performed at every successive station. It may be
done by a magnetic needle or by the back-sighting method. The back-sighting is
process is always preferred because it is reliable.

19. Orienting The Plane Table :-
The operation of keeping the table at each of the successive stations parallel to the
position which it occupied at the first station is known as orientation.
It is necessary when the instrument has to be set up at more than one station.
It is based on parallelism & relative position of an objects on the map will be
accurate only if the orientation is proper.
There are two methods of orienting the table:
1.Orientation by the Magnetic Needle :- This method is used when it is not
possible to bisect the previous station from the new station. This method is
not much reliable and prone to errors due to variations of magnetic field.
2.Orientation by Back-sighting :- In this method the table is orientated by
back sighting through the ray which is drawn from the previous station.
This is the most accurate and reliable method of orientation of plane
table.

20. Orientation by the Magnetic Needle :-
1)Suppose A & B are two stations. Plane table is set up at station A, & leveled by
spirit level. Centering is done by U-fork & plumb bob so that point ‘a’ is just over
the station A. Then the compass is placed on the right hand top corner of the sheet
in such a way that he needle coincides with 0-0 mark. After this a line
representing north line is drawn through the edge of the compass box.
2)With the alidade touching the point ‘a’ the ranging rod at B is bisected & a ray
is drawn. The distance AB is measured & plotted to any suitable scale.
3)Table is shifted & centered over B, so that point ‘b’ is just over B. The table is
leveled. Now the trough compass is placed exactly along the north line drawn
previously. Table is then turned clockwise or anticlockwise until the needle
coincides exactly with 0-0 mark of the compass.
4)When the centering & leveling are perfect & the needle is exactly at 0-0 the
orientation is said to be perfect.

22. Orientation by Back-sighting :- Accurate & Preferred
1)Suppose A & B are two stations. Plane table is set up over ‘A.’ The table is leveled
by spirit level & centered by U-fork so that the point ‘a’ is just over station ‘A.’ The
north line is marked on the right hand top corner of the sheet by trough
compass.
2)With the alidade is touching the ranging rod at ‘B’ is bisected & ‘a’ ray is drawn.
The distance AB is measured & plotted to any suitable scale. So the point ‘b’
represents stations B.
3)The table is shifted & set up over B. It is leveled & centered so that ‘b’ is just over
B. Now the alidade is placed along the line ‘ba’ and the ranging rod at ‘A’ is
bisected by turning the table clockwise or anticlockwise.
4)At this time the centering may be disturbed & should be adjusted immediately if
required. When centering, leveling & bisection of ranging rod at ‘A’ are perfect
then the orientation is said to be perfect.

24. There are four methods of surveying with the Plane Table:
1)Radiation Method
2)Intersection Method
3)Traversing Method
4)Resection Method

Radiation Method :-
A ray is drawn from the instrument station towards the point and is located by
plotting to some scale the distance so measures.
This method is suitable for the survey of the small areas which can be commanded
from a single station.
It is chiefly used for locating the details from station which have been previously
established by other methods of surveying such as triangulation.

25. Radiation Method :-
The objects are located by radiating lines from the point, and measuring the distance
with chain or tape with suitable scale.

A
C
B
F
E
a
b
c
d
e
f
P

26. Intersection Method :-
1)The point is fixed on the plane by the intersection of the rays drawn from the two
instrument stations.
2)The line joining the stations is called Base line.
3)The method requires only the linear measurements of this line (Base Line)
4)This method is commonly adopted for locating the details, distance, inaccessible
points, broken boundaries, rivers & points which may be used subsequently as the
instrument station.
5)It is suitable when it is difficult or impossible to measure distance as in the case
of the survey of a mountainous country. It is also used for checking distant objects.

27. Traversing Method :-
1) At each successive station is set & foresight is taken to the following station & its
location is plotted by measuring the distance between two station as in the radiation
method. Hence, the traversing is not much different from radiation as for working
principle is concerned.
2) It is also similar to that of Compass Survey or Transit Traversing.
3)It is widely used for running survey lines between stations, which have been
previously fixed by other methods of survey, to locate the topographic details.
4)Suitable for the survey of roads, rivers, etc.

28. Resection Method :-
1)This method is used for establishing the instrument stations only in order to
locate missing details.
2)After fixing the stations, details are located either by radiation or intersection.
3)The characteristics features of resection is that the point plotted on plan is the
station occupied by the plane table.

29. Special Methods of Resection :--
Sometimes after the completion of plane table traversing, it may be noticed that an
important object has not been located due to oversight.
If no station pegs are found on the field, some special methods of resection are a
applied in order to establish a new station for plotting the missing object.
1)The Two Point Problem
2)The Three Point Problem

30. Special Methods of Resection :--
The Three Point Problem:
Three well defined points are selected whose positions have already been plotted on
the map.
Then by perfectly bisecting these three well defined points, a new station is
established at the required position.
No auxiliary station is required in order to solve this problem.
Table is directly placed at the required position.

a)Bessel’s Method or Graphical Method
b)Mechanical Method or Tracing Paper Method
c)Trail & Error Method

31. Three Point Problem :- Graphical or Bessel’s Method
1)Suppose A, B & C are three well defined points which have been plotted as a, b & c.
Now it is required to locate a station P.
2)The table is placed at the required station P and levelled. The alidade is placed along
the ca and the point A is bisected and the table is clamped. With the alidade centred
on C, the point B is bisected and ray is drawn. (Fig. a)
3)Again the alidade is placed along the line ac and the point C is bisected and the
table is clamped. With the alidade touching a, the point B is bisected and a ray is
drawn. Suppose this ray intersects the previous ray at a point d. (fig. b)
4)The alidade is placed along db and the point B is bisected. At this position the table
is said to be perfectly oriented. Now the rays Aa, Bb and Cc are drawn. These three
rays must meet at a point p which is the required point on the map. This point is
transferred to the ground by a U-fork and plumb. (fig. c)

33. Three Point Problem :- Graphical or Bessel’s Method
The table is placed at the required station P and levelled. The alidade is placed along the
ca and the point A is bisected and the table is clamped. With the alidade centred on C,
the point B is bisected and ray is drawn. (Fig. a)







Again the alidade is placed along the line ac and the point C is bisected and the table is
clamped. With the alidade touching a, the point B is bisected and a ray is drawn.
Suppose this ray intersects the previous ray at a point d. (fig. b)

34. Three Point Problem :- Mechanical or Tracing Paper Method
1)Suppose A, B & C are three well defined points which have been plotted on the maps
as a, b & c. Now it is required to locate a station P.
2)The table is placed at the required station P and levelled. A tracing paper is fixed on
the map and a point is marked on it.
3)With the alidade centred on P, the points A, B and C are bisected and rays are drawn.
These rays may not pass through the points a, b and c as the orientation is done
approximately. (Fig. a)
4)Now the tracing paper is unfastened and moved over the map in such a way that
the three rays simultaneously pass through the plotted position a, b and c. then the
points p is pricked with pin to give an impression p on the map. P is the required
point on the map. The tracing paper is then removed. (fig. b)
5)Then the alidade is centred on p and the rays are drawn towards A, B & C. These
rays must pass through the points a, b and c.

36. Three Point Problem :- Mechanical or Tracing Paper Method
With the alidade centred on P, the points A, B and C are bisected and rays are drawn.
These rays may not pass through the points a, b and c as the orientation is done
approximately. (Fig. a)






Now the tracing paper is unfastened and moved over the map in such a way that the
three rays simultaneously pass through the plotted position a, b and c. then the points
p is pricked with pin to give an impression p on the map. P is the required point on the
map. The tracing paper is then removed. (fig. b)

37. Three Point Problem :- Mechanical or Tracing Paper Method
Now the tracing paper is unfastened and moved over the map in such a way that the
three rays simultaneously pass through the plotted position a, b and c. then the points
p is pricked with pin to give an impression p on the map. P is the required point on the
map. The tracing paper is then removed. (fig. b)







Then the alidade is centred on p and the rays are drawn towards A, B & C. These rays
must pass through the points a, b and c.

38. Three Point Problem :- Trial and Error Method
1)Suppose A, B & C are three well defined points which have been plotted on the maps
as a, b & c. Now it is required to locate a station P.
2)The table is placed at the required station P and levelled.
3)With the alidade, rays Aa, Bb and Cc are drawn. As the orientation is approximate,
the rays may not intersects at a point, but may form a small triangle. (triangle of
error)
4)To get the actual point, this triangle of error is to be eliminated. By repeatedly
turning the table clockwise or anticlockwise, the triangle is eliminated in such a
way that the rays Aa, Bb and Cc finally meet at a point p. This is the required
point on the map. This point is transferred to the ground by U-fork and plumb bob.

40. Three Point Problem :- Trial and Error Method
With the alidade, rays Aa, Bb and Cc are drawn. As the orientation is approximate,
the rays may not intersects at a point, but may form a small triangle. (triangle of
error)






To get the actual point, this triangle of error is to be eliminated. By repeatedly turning
the table clockwise or anticlockwise, the triangle is eliminated in such a way that the
rays Aa, Bb and Cc finally meet at a point p. This is the required point on the map.
This point is transferred to the ground by U-fork and plumb bob.

41. Two Point Problem :-
1)Well defined 2 points whose positions have already been plotted on the plan are selected. Then
by perfectly bisecting these points, new station is established at the required position.
2)Suppose P & Q are two well defined points whose positions are plotted on the map as p & q. It
is required to locate a new station at A by perfectly bisecting P & Q.
3)An auxiliary station B is bisected at a suitable position. The table is set up at B & levelled
and oriented by eye estimation. It is then clamped.
4)With the alidade is touching p & q, the points P & Q are bisected and rays are drawn.
Suppose these rays intersect at b.
5)With the alidade centred on b, the ranging rod at A is bisected and a ray is drawn. Then, by
eye estimation a point a1 is marked on this way.
6)The table is shifted and centred on A, with a1 just over A. It is levelled and oriented by
back-sighting. With the alidade touching p, the point P is bisected and a ray is drawn.
Suppose this ray intersects the line ba, at the point a1, as was assumed previously.
7)With alidade cantered on a1, the point Q is bisected & a ray is drawn. Suppose this ray
intersects the ray bq at a point q1. Triangle pqq1 is triangle of error & is to be eliminated

42. The Two Point Problem

43. Two Point Problem :-
8)Alidade is placed along line pq1 & ranging rod R is fixed at some distance from the
table. Then the alidade is placed along the line pq and the table is turned to bisect R.
At this position, the table is said to be perfectly oriented.
9)Finally, with alidade centred on p & q, the points P and Q are bisected & rays are
drawn. Suppose these rays intersects at a point a. This would represent the exact
position of the required station A Then the station A is marked on the ground.

44. Errors in Plane Table Surveying :--
1)The table should accurately centred.
2) The rays should be accurately drawn through the station points.
3) Table should be sufficiently clamped.
4) The board should be horizontal.
5) The objects should be accurately sighted.

Following precautionary measures should be taken while performing field work:
a) The table must be accurately oriented once the table is shifted.
b) The alidade should be correctly centred on the station point on paper.
c) The expansion and contraction of paper should be taken care off.

45. Area & Volume Calculation :--
1)The Selection of method for calculation area and volume depends on shape and
accuracy required.
2)Planimeter are used to find out the area of irregular shapes.
3)Volume of earthwork, volume of reservoir, etc.

46. End Area Formula: Trapezoidal Formula

V = L [ ( ( A
1 + A
n ) / 2 ) + ( A
2 + A
3 + A
4 + …… A
n-1 ) ]
A
1, A
2, A
3, A
4, .…… , A
n are the end consecutive areas.
L is the distance between them.

47. Prismoidal Formula: Simpson’s rule.









V = L / 3 [ ( A
1 + A
n ) + 4( A
2 + A
4 + …… A
n-1 ) + 2(A
3 + A
5+ A
7 +……..+A
n-2 ) ]
A
1, A
2, A
3, A
4, .…… , A
n are the end consecutive areas.
L is the distance between them.

48. Q1)Following perpendicular offsets were taken from a chain line to a hedge, Calculate area
between survey line, a) Trapezoidal Rule b) Simpsons rule




Sol: a) Trapezoidal Rule
From I to V interval is constant (d
1 = 15m) A
1
From V to VII interval is constant (d
2 =10m) A
2
From VII to X interval is constant (d
3=20m) A
3
A
1 = ( ( 7.6 + 10.6 ) / 2 + 8.5 + 10.7 + 12.8 ) * 15 = 616.3 m
2
A
2 = ( ( 10.6 + 8.3 ) / 2 + 9.5 ) * 10 = 189.5 m
2

A
3 = ( ( 8.3 + 4.4 ) / 2 + 7.9 + 6.4 ) * 20 = 413 m
2

A = A
1 + A
2 + A
3 = 1219 m
2


Chainage, m 0 15 30 45 60 70 80 100 120 140
Offsets, m 7.6 8.5 10.7 12.8 10.6 9.5 8.3 7.9 6.4 4.4

49. Q1)Following perpendicular offsets were taken from a chain line to a hedge, Calculate area between
survey line, a)Trapezoidal Rule b)Simpsons rule


Sol: a)Trapezoidal Rule
A = 1219 m
2

From I to V interval is constant (d
1 = 15m) A
1
From V to VII interval is constant (d
2 =10m) A
2
From VII to X interval is constant (d
3=20m) A
3
b) Simpsons rule
A
1 = 15 / 3 ( ( 7.6 + 10.6 ) + 4 ( 8.5 + 12.8 ) + 2 ( 10.7 ) ) = 624 m
2

A
2 = 10 / 3 ( ( 10.6 + 8.3 ) + 4 ( 9.5 ) ) = 189.7 m
2

A
3 = 20 / 3 ( ( 8.3 + 6.4 ) + 4 ( 7.9 ) ) + ( ( 6.4 + 4.4 ) / 2 ) * 20 ) = 416.6 m
2

A = 1230.3 m
2

Chainage, m 0 15 30 45 60 70 80 100 120 140
Offsets, m 7.6 8.5 10.7 12.8 10.6 9.5 8.3 7.9 6.4 4.4

50. Q2)The following perpendicular offsets were taken from chain line to an irregular boundary. Calculate
the area between the chain line, the boundary & the end offsets.




Ans: A
1 = ( ( 10 – 0 ) / 2 ) * ( 15.5 + 26.2 ) = 208.5 m
2
A
2 = ( ( 25 – 10 ) / 2 * ( 31.8 + 26.2 ) = 435 m
2
A
3 = 487.9 m
2
A
4 = 491.4 m
2
A
5 = 453.7 m
2
Total Area , A = 2076.5 m
2
Chainage, m 0 10 25 42 60 75
Offset, m 15.5 26.2 31.8 25.6 29 31.5

51. Q3) Following perpendicular offsets were taken from a chain line to an irregular boundary. Calculate
area between chain line and irregular boundary by a)Trapezoidal Rule b)Simpsons rule.



Ans.:-
Trapezoidal Rule area =790.5 m
2
Simposons Rule Area, A
A
1 = 30 / 3 ( ( 0 + 5 ) + 4 ( 2.65 + 3.75 + 3.6 ) + 2 ( 3.8 + 4.65 ) ) = 619 m
2
A
2 = ( 5 + 5.8 ) / 2 ) * 30 = 162m
2
A =A
1+A
2= 781 m
2
Chainage 0 30 60 90 120 150 180 210
Offset length 0 2.65 3.80 3.75 4.65 3.6 5 5.80