plane table surveying covers the Concept of surveying

PLANE TABLE SURVEYING ,
DEFINITION
PRINCIPLE
INSTRUMENTS
ERRORS
ORIENTATION
METHODS

1. VN.P. ENGINEERING COLLEGE

Dr. Hitesh R. Ashani
Assistant Professor
Department Of Civil Engineering

2. GUJARAT TECHNOLOGICAL UNIVERSITY
Bachelor of Engineering
Subject Code:3140601
Semester IV
SURVEYING

Type of course: Professional Core course

Rational: To develop concepts of various types of land surveying and prepare and interpret maps and
drawing

Teaching and Examination Scheme:

Teaching Scheme | Credits Examination Marks Total
L T P G Theory Marks Practical Marks Marks
ESE PA ESE PA

Œ) M Viva (V) (0)

4 0 2 5 70 30 30 20 150

3. Content:
Module. . No. of | Weightage
No. Tops Hours | (%)

1

Plane Table Survey: Introduction, principle, instruments, setting up the
plane table, methods of plane tabling, advantages, sources of Errors.

Theodolite Traversing: Introduction, definitions, the Vermer
transit theodolite, temporary and permanent adjustment of theodolite,
2 |measurmg honzontal and vertical angles, methods of traversing, | 8 15
closing error, computation of latitudes and departure, check in closed

and open traverse, balancing of traverse, Gale’s table.
Trigonometric levelling: Indirect levelling, heights and distances,

3 methods, direct levelling on steep ground. ’ $
Curves: Introduction, classification of curves, Elements of a simple
4 circular, designation of curve, methods of setting out a simple circular 3 15

curve, elements of a compound and reverse curves, transition curve,
types of transition curves, combined curve, types of vertical curves.

4. Areas and Volumes: Introduction, computation of area, computation of
area from field notes and plotted plans, boundary area, area of traverse,
Use of Plannimeter, computations of volumes, Volume from cross
sections, Trapezoidal and Prismoidal formulae, Prismoidal correction,
Curvature comection, capacity of reservoir, volume from borrow pit.

Tachometric Surveying: Introduction, purpose, principle, instruments,
methods of tacheometry, stadia constants, anallatic lens, Subtense bar,
field work in tacheometry, reduction of readings, errors and precisions.

Geodetic Surveying: Introduction, triangulation, principle and uses of
triangulation, trangulation systems and its classification, well-
conditioned triangles, strength of figure, selection of triangulation
stations and their infer-visibility, stations marks, signals, towers and
scaffolds, base line, site selection and base line measurement, tape
corrections, the base net, extension of base line, satellite station and
reduction to centre.

Theory of Errors : Introduction, types of errors, definitions, laws of
accidental errors, laws of weights, of least s, rules for

5. caving weights and distibution of errors to the field observations,
determination of the most probable values of quantities.

Modern Surveying Instruments: Introduction, electromagnetic

spectrum, electromagnetic distance measurement, types of EDM

2 instruments, electronic digital theodolites, total station, digital levels, a
scanners for topographical survey, global positioning system.
Suggested Specification table with Marks (Theory): (For BE only)
Distribution of Theory Marks
R Level ULevel ALevel NLevel | Elevel | CLevel
10% 10% 50% 10% 10% 10%

Legends: R: Remembrance; U: Understanding; A: Application, N: Analyze and E: Evaluate C:

Create and above Levels (Revised Bloom’s Taxonomy)

Note: This specification table shall be treated as a general guideline for students and teachers. The actual
distribution of marks in the question paper may vary slightly from above table.

6. List of Experiment:
+ Plane table traversing by intersection and radiation methods
© Techeometry Survey Project.
+ Theodolite traversing and plotting of traverse by applying corrections in Gale’s traverse table
+ Setting out simple circular curve by different methods
© Setting out combined curve (Transition - Circular — Transition)
* Computation of area of submergence and storage volume from contour maps for reservoir
projects.
+ Introduction to modern surveying Instruments.

7. Reference Book:

Title Author/s Publication

Surveying and levelling N.N. Basak Tata Mcgraw Hill, New Delhi

Surveying -Volume LI &II Dr. KRArora | Standard Book House, New Delhi

Surveying, Volume-I, I & II B.C Punma Laxmi Publications, New Delhi

Surveying and Levelling, Volume 1 & II | T.P. Kanetkar and | Pune Vidyarthi Griha Prakhashan, Pune

S.V Kulkarni

Surveying and Levelling RSubramanian | Oxford University Press, New Delhi

Surveying Vol. I and II S. K. Duggal Tata Mcgraw Hill, New Delhi

Advanced Surveying R Agor Khanna Publishers. New Delhi

Surveying and Levelling R Agor Khanna Publishers, New Delhi
Web Material Links:

e http://nptel.ac.in/courses/105

07122/

e http://nptel.ac.in/courses/105

07157/

e http://nptel.ac.in/courses/105

01087/

e http://nptel.ac.in/courses/105104100/

e www.svnit.ac.in

8. After vote course the students will be able to:
r

CO Numbe: Course Outcomes cL
C3140601.1 |Perform plane table, traverse, trigonometric & tacheometric surveying. Ap
C3140601.2 [Practice setting out curves. Ap
C3140601.3 |Calculate the area and volumes of engineering works Ap
C3140601.4 [Explain (with example) aspects of geodetic surveying. U
C3140601.5 Apply theory of errors for calculate the most probable value and distribution Ap
of error
C3140601.6 |Describe modern tools for surveying. U

9. PLANE TABLE SURVEYING

Total Hours : 04
Weightage in GTU : 8 % (5 to 7 marks)

10. After learning this chapter student will be
able to...

11. + A plane table surveying is a graphical
method of surveying.

+ In this method of surveying....
+ field observation (distance between instrument
station and object) and
* Drawing / plotting are done one by one,
helping the surveyor to compare the drawing
details with actual features of the ground.

+ — It is simple and cheaper than theodolite survey.
+ — It is most suitable for small scale maps.

+ The plan is drawn by the surveyor in the field,
while the area to be surveyed is before
surveyor’s eyes.

12. It is one of the most rapid and less costly
than theodolite surveying.

As surveying and drawing are done one
by one in the field, chances to forget of
any detail get less.

The plotting details can immediately get
compared with the actual objects present
in the field.

The surveyor can check the accuracy of

his work more frequently and from any

position he may desire, thus eliminating
all error at the spot.

13. 10.

Contours and specific features can be represented
and checked conveniently as the whole area is in view
at the time of plotting.

Only related details are located because the map is
drawn as the survey progresses. Irrelevant details get
omitted in the field itself.

It is particularly suitable for filling in details in hilly
areas and in magnetic areas where chain and compass
surveys are not suitable.

The instruments used are simple.

skill for operation of instruments is not required.

Field book is not required.

14. The plane table survey is not possible in
unfavorable climates such as rain, fog etc.

This method of survey is not very accurate and
thus unsuitable for accurate work.

As no field book is maintained, plotting at
different scale require full exercise.

The method requires large amount of time to
be spent in the field.

Quality of the final map depends largely on the
drafting capability of the surveyor.

This method is effective in relatively open
country where stations can be sighted easily .

15. PRINCIPLA OF PLANE TABLE SURVEYING

* Plane table surveying is based on the principle that lines drawn on
paper/sheet (between paper station and object) are always parallel to the
corresponding lines actually present on the ground between ground station
and ground object

16. Instruments
(GTU - 2009 , 2010 ,2011)

+ 1.plane table with tripod
+ 2.alidade

+ 3.spirit level

+ 4.through compass

+ 5.u-fork or plumbing fork

sy

Plan Table: (drawing board made
well-seasoned wood with its upper surfa
exactly planed. It is normally rectangul:
shape with size 75 cm x 60 cm)

e table.

esy: http://2.bp.blogspot.com

17. Plane Tables

The plane table consists of a drawing board
with arrangement for fixing on a tripod
stand.

Size - 750 x 600 mm

Thickness of board — 20 mm

Top surface is well leveled

Bottom surface consists of threaded circular
plate for fixing plane table on tripod.

18. Plane Tables

+ Used for fixing a drawing sheet over it

* There are various types of plane
tables, depending upon the

+ 1.arrangement of fixing
+ 2. leveling of the table and

+ 3.rotating arrangement in a
horizontal plane.

+ 1.simple plane table
+ 2.johnson plane table
+ 3.coast survey plane table

19. + It is a small drawing board mounted on light
tripod

+ It can be rotated in horizontal plane about
vertical axis and fixed in any position

+ Used for small survey work

+ Levelling of table -done using tripod legs by
eye observation.

20. Johnson plane table

* Size of drawing board -600 x 450 mm or 750
x 600 mm

* consist of ball and socket arrangement and
vertical spindle with two thumb screw

* Ball and socket arrangement is operated by
upper thumb screw

+ When Upper screw is free — table can be
rotated in vertical plane for levelling

+ When Lower screw is free - table can be
rotated in horizontal plane for orientation

+ Use for accurate survey of large area.

21. Cost survey plane table

+ Most accurate plane table
* Levelling is done by three foot screw

* Table can be rotated in horizontal for orientation and vertical
direction for levelling with clamp and tangent screw.

22. Alidade

+ An alidade is a straight edge ruler having
some sighting device.

+ It is used to draw a line parallel to the line of
sight and thus provides the direction of the
object to be plotted.

+ Depending on the type of sighting
arrangement, alidades are classified as

+ 1.Plain Alidade
« 2.Telescopic Alidade

OBJECT VANI
SIGHT VANE

BEVELLED EDGE

Alidade with components

24. Plane alidade

+ Straight edge ruler 450 mm long made of
metal or wood

* One edge is beveled and graduated and is
known as fudicial edge

* Consists two vane - eye vane and object vane
hinged with ruler

+ Eye vane provided with — narrow slit

+ Object vane provided with — wide slit & horse
hair

* Object vane when unfolded — it is
perpendicular to the ruler.

+ Used for small scale and when accuracy is not
required.

4— Eye vane Object vane

}

Fiducial edge Bevelled edge

25. Telescopic alidade

«Used when inclined sight is there in Bubbie tuve
field

*Consists of telescope for inclined
sighting object located fare away

“Vanes are not provided but fudicial

edge is provided

*Telescope is provided with stadia
diaphragm - and can be used to find
distance and elevation.

«Line of sight of telescope and fudici
edge are parallel to each other

26. Spirit level

* It consists of flat based tube with a À
small bubble either circular or tubular
in shape.

* It is used to check the level of plane
table by placing it on the board in two À
positions at right angles to each
other.

+ When the bubble remains in the $
centre at any point on the table, it is
considered to be properly levelled.

27. Through compass

* A trough compass consists of a long, narrow
rectangular box, covered with glass.

Inside the box, at its centre, there is a magnetic
needle resting on the pivot.

At the extremities of the trough compass, there
are graduated scales with zero at the centre and
marking up to 5° on either side of the zero line.

The trough compass is used for marking the
magnetic north line on the drawing sheet of the
plane table.

In this case, the magnetic needle point to 0° - 0°
of the graduated scale and a line drawn parallel
to the edge of the trough compass is along the
magnetic meridian.

A trough compass is also used to orient the
plane table with respect to the magnetic
meridian.

Wooden box
Graduations

LA

_—

Pivot

Magnetic
needle

28. U —fork of plumbing fork

+ It is a metal strip bent in the shape
of “U” having equal arm length.

+ Top arm is pointed and bottom arm
with hook to attaché plumb bob.

« Used for transferring of the ground
point on the drawing sheet - when
plane table is centered over ground.
Req. point on the sheet is given by
pointed end of upper arm

« For centering table — when point of
upper arm is kept over plotted point fork
on sheet , the plumb bob is exactly
over the station peg.

Fig. 14.4. Plumbing fork and plumb bob.

29. Source of error

+ 3 types of error:

+ 1. instrumental error
+ 2. personal error

+ 3. error in plotting

+ 1. instrumental error

+ Top surface of plane table is not perfect plane
+ Fiducial edge of alidade is not straight

+ Fitting of table and tripod is loose

* Needle of compass is not properly balanced

* Object vane not perpendicular to fiducial edge
+ Horse hair loose

* Level tube is defective

+ Drawing paper — not of good quality

30. + 2. personal error

* Plane table — not properly levelled

+ Plane table is not accurately centered

* Orientation of plane table is not proper

* Object — not bisected properly

* Alidade not touching the station on paper while bisection
* Rays drawn by alidade is not perfect

« Alidade not pivoted with same side during whole work

31. + 3. error of plotting

* Incorrect scale is used

* Good quality pencil with fine pointed end not used
* Incorrect measurement from the scale

* Speed at the time of plotting

+ Using wrong method of plotting

32. Setting up the plane table
(GTU—2011, 2012)

« At each station, the plane table is required to get set up before
carrying out any plotting work. It basically consists of the operations:

+ 1. fixing,

+ 2.centring

« 3. levelling

+ A. marking the north line
+ 5. orientation

33. Fixing the plane table on tripod stand

+ In this operation, first the top
of the tripod stand is fixed in
level by eye estimation at
convenient height with its legs
uniformly spread and shoes
fixed firmly into the ground.

+ The board is fixed to the tripod
head by tightening the
clamping screw.

34. Levelling plane table

* The top of the table is levelled
by moving the legs of the
tripod.

* The level of plane table is first
judged by eye estimation.

* Further, it is checked by
keeping spirit level at different
positions on the table and if
required, legs are further
adjusted.

Adjusting the tripod

35. Centering of plane table

«there are two types of operations
involved in centring of plane table.

¢1.the centering with reference to
already plotted position of the
station.

+ In this case, the pointed end of the
upper arm of a U-fork is held at the
plotted position of the station and
the table is shifted and adjusted in
such a way that the tip of the plumb
bob points exactly over the ground
station.

Upper arm
|

37. Centering of plane table

« 2.the centring with reference to
ground location of the station.

+ In this case, the tip of the plumb
bob attached to a U-frame is
placed exactly over the ground
point which is required to be
transferred.

+ The point corresponding to the
tip of the pointed arm of the U-
frame provides the transferred
position on the table.

Upper arm
|

| Point rd

A
Plumbing 4 Sp
fork
Plumb
bob
=)

38. Marking north line

* Through compass is placed on right hand top corner of drawing
sheet.

* Compass is turned clockwise or anticlockwise so that the needle
exactly coincides with the O- O mark.

+ At this time line is drawn through edge of the compass that represent
north line.

39. orientation

+ When in survey no. of stations are there , orientation is required.

+ Means — setting up plane table at each of successive station as per
the same direction it occupied at the previous station.

40. Methods of orientation

« During orientation, the levelling of the plane table generally gets
disturbed so it is usually carried out with levelling simultaneously.

+ The orientation of plane table can be carried out by
* trough compass
* back sighting

41. Using through compass

* In this method, the edge of the trough compass is placed along the
north line also known as magnetic meridian (drawn at the starting
station on right hand top corner ) and the plane table is rotated in
horizontal plane till the needle points to zero-zero reading in the
through compass.

+ Once it is achieved, the table is said to be oriented and thus
clamped.

+ This method of orientation is not very accurate and also may get
affected by local attraction and is generally used for small-scale
survey.

42. Using back sighting

+ In this method, the Fiducial edge
of alidade is laid along a ray Bananen

drawn from previous station to 1
the present station and the plane E E

table is then rotated till the line of b
sight of alidade bisects exactly the Ñ

ranging rod placed at previous
station.

1
+
|
A

«The plane table is then clamped
and said to be oriented. In this SR EURE
method, the level of the plane LE GWORIECTVANE
table has to be maintained equal Sie ae
in both the stations.

43. Methods of plane table surveying

+ To carry out the operations under different field conditions, different
methods of plane table surveying have been evolved

method of radiation
method of intersection
method of traversing
the method of resection

Pe Nh

44. Radiation method

+ In the radiation method of plane table surveying, the direction of the
objects or points to be located are obtained by drawing radial lines
along fiducial edge of alidade after getting the objects or points
bisected along the line of sight of the alidade.

+ The horizontal distances are then measured and scaled off on the
corresponding radial lines to mark their positions on the drawing.

45. + A point P is to be selected in such a
way that all the other points (ABCD
E) are seen easily from P.

+ Mark the direction of the North on
the sheet by using compass

+ Locate instrument station p on the
sheet by using plumbing fork, such
that p on sheet is exactly over P on
ground

+ At first, by putting the alidade
touching station p of drawing sheet ,
ground station A is bisected using
alidade.

«Distance between P and A is
measured on ground using tape.

46. « After measuring the distance
of PA on field, the
measurement needs to be put
on paper to a suitable scale.

* Now measure the distances of =

each point from P i.e., PB, PC, fo
PD, PE and plot them to scale p

on the sheet as, pb, pc, pd, pe

respectively.

«Points a, b, c, d, and e are
joined on drawing sheet as
shown in figure.

47. Intersection Method

* In intersection method of plane table surveying, the objects or points
to be located are obtained at the point of intersection of radial lines
drawn from two different stations.

+ Used ....

+ when distance between station and object is large can not be measured
accurately,

+ in hilly area,
+ For small scale survey,

48. Intersection Method

* Select two stations O1 and O2 so
that the points to be located on
paper are easily seen from them.

«The table can be centered and
leveled at station O1 and then after
orienting at station O2, the distance
0102 can be accurately measured
and put up to some scale on the
paper.

* Plotted line 0102, which is known as o 0, 0; 0
the base line, on paper Plane table at O, Plane table at O,

. Fig. 14.8. Intersection method of plane tabling
*From station O1, draw rays for

stations A, B, etc

49. Intersection Method

+ Shift the table to station O2 and
after proper orientation, take rays
of stations A, B etc.,

«The intersection of rays from
stations 01 and 02 will give points
a, b etc. on paper, as shown in
figure.

+ For checking the accuracy of work,
measure the distance AB on
ground and compare it with its
corresponding length ab on paper.

% % 9 o
Plane table at O, Plane table at O,

Fig. 14.8. Intersection method of plane tabling

50. Plane Table Traversing

* This method of plane table surveying is used to plot a traverse in
cases stations have not been previously plotted by some other
methods.

+ In this method, traverse stations are first selected.

* The stations are plotted by method of radiation by taking back sight
on the previous station and a fore sight to the following station.

* Here distances are generally measured by tachometric method and
surveying work has to be performed with great care.

51. Plane Table Traversing

52. Plane Table Traversing

* Let us consider the stations P,Q, R and S
which are to plotted by method of
traversing.

+ Stations are to be chosen in such a way
that adjoining stations are visible.

+ First, the plane table is to be set at
station P and then plotted as p.

+ With the alidade pivoted at p, draw the
rays from p to Qand S.

+ Distances PQ and PS on ground are
measured and plotted on the respective
rays, as pq and ps respectively.

53. Plane Table Traversing

+ The plane table is then shifted to
station Q, get it set and then
oriented by back sighting to
station P.

«With the alidade pivoted at q,
draw a ray to R.

* Distance QR is measured and
plotted on the ray as qr.

+ In this way, plane table is shifted
to stations R and S and
corresponding rays are drawn to
obtain the plotting of the traverse
pars.

54. Resection

+ This method of plane table surveying is employed to locate and plot the
position of the plane table during surveying.

+ This also results in the orientation of the plane table.

+ The basic principle of resection is opposite to that of the method of
intersection.

+ In this method, the position of the plane table is determined by drawing
resectors from already plotted points.

+ There are different methods for locating plane table by method of resection
and are primarily based on the type of orientation which precedes resection.

55. Resection

«The process of locating the instrument station
occupied by the plane table by drawing rays from
the stations whose positions have already been
plotted on the drawing sheet.

«The resection of two rays will be the point
representing the station to be located, provided the
orientation at the station to be plotted is correct,
which is seldom achieved.

56. Resection

+ Various methods to solve the problem of orientation
+ Back ray
+ Two point
+ Three point
* Suitability:
+ Used when during surveying surveyor feels that some important details can
be plotted easily by choosing any station other than the triangulation

stations.
+ The position of such station is fixed on the drawing sheet by resection.

57. Resection after orientation by back ray
* Resection after Orientation by Back ray:

+ Figure shows the procedure of resection
after orientation by back sighting. B

+ From station A, the position of B is plotted
as ‘b’

+ and ray has been taken to station P as ap’.

* Then plane table is set at P and oriented
by back sighting A, line AP is not measured
but the position of P is obtained on the
paper by taking resection Bb.

58. Resection after orientation by back ray

oy
ES
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Y x
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£ x
/ CAC
£ $
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Y x
7 \
7 x
£ x

Stn A Stn P

59. Resection after orientation by two points

+ The problem of finding plotted position of the station point occupied
by the plane table with the help of plotted positions of two well
defined points is known as solving two point problem. Figure shows
the scheme of solving this.

60. Resection after orientation by two points

* Let O, O, be the two stations plotted as o, and o, on the

drawing sheet. It is required to plot station Oj for plane tabling
work.

Rotation of Table at O,.

61. Resection after orientation by two points

*A point A on ground is selected such that AO, is approximately
parallel to O, O, and the angle O, O, A and 0, O, A are balanced
angles.

* The table is set and levelled at A, and so oriented that line O,

O, on ground is nearly parallel to line o, o, plotted on table
map.

21.2

/
Zo'¿0,0, is Orientation Error;

Rotation of Table at O,

62. Resection after orientation by two points

* Alidade, touching o, and sighting O, on ground, a ray is drawn

through o,. In the same way, draw a ray by touching alidade to

o, and sighting O, on ground. This ray will intersect the first ray
at a, on the map.

A penne ee ee eee eee een eee eee eens 7 Op
E ~ vod
x ae e 1
,

- i
5. £0',0,0, is Orientation Error /

Rotation of Table at O,.

63. Resection after orientation by two points

+ With alidade touching a,, sight Oz and draw the ray a, 03. Mark
the estimated position of O, on the map as 0”.

Rotation of Table at O,.

64. Resection after orientation by two points

* The table is removed from A and set at O, with marked position
of 0’, over O,, properly levelled and similarly oriented. This is
achieved by back sighting A from O..

Rotation of Table at O,.

65. Resection after orientation by two points

* Now with table at O,, keep alidade touching o, and sight O, and
draw a back ray resecting the line a, 0’; in 03. Here oz is the
point representing the station O, with reference to the
approximate orientation made at A.

Rotation of Table at O,.

66. Resection after orientation by two points

+ With alidade touching 03, sight O, and draw a ray to O,. If the
ray passes through the plotted point o,, the orientation of the
table is correct and oz is the correct position of O;. Whereas, if
this ray cuts the previously plotted line a, 0, at some other
point, say o”,, then the position o, is not the correct position of

Rotation of Table at O,.

67. Resection after orientation by two points

* The orientation error will be equal to 4o”,0,0, between the
lines o, 0, and o, o,'. This error can be eliminated by rotating
the table through the angle 0,’ 0, 0,. This table rotation can be
achieved by taking the following steps.

Rotation of Table at O,.

68. orientation by two points: Elimination of error

* The alidade is placed along line o, 0,’ and a ranging rod Bis
fixed in line with o, 0,', far away from the plane table.

Rotation of Table at O,.

69. orientation by two points: Elimination of error

* Alidade is now kept along true line o, o, and table is rotated so
that ranging rod B is bisected. The table is clamped in new
position.

Rotation of Table at O,.

70. orientation by two points: Elimination of error

+ The true location of O3 on map is now marked by :
* (a)orienting alidade along o, O, and drawing the ray o, O,, and
* (b) orienting alidade along o, O, and drawing the ray 0, O,.

¢ The point of intersection of the two rays will give the correct position
of O, (the new table position) on map.

Rotation of Table at O,.

71. orientation by two points: Elimination of error

* The new position of table station O, is, thus, correctly marked
on map with the help of two previous table stations O, and O,
already marked on map. The procedure followed is termed
two-point problem in plane table survey.

Rotation of Table at O,.

72. Three point problem:

* The position of new plane table station on the map can be correctly
located with the help of three well defined points on ground whose
positions are already plotted on map.

+ Such a procedure is called three-point problem.

* It is obvious that locating the position of table by this process is more
accurate. However, it is more complex.

73. Three point problem:

* This can be achieved by any of the following methods :

* (a) Mechanical
* (b) Graphical
+ (c) Trial and Error

74. Three point problem:

* The method is based on the fact that, in a correctly oriented plane
table, resectors through well defined points get intersected at a point
which represents the location of the plane table station on the
drawing.

75. Three point problem

+ Set the table over station P and
by observation approximately
orient the table.
«Fix the tracing paper on the
plane

table and

select P
approximately, say as p’.

« From p’, draw p' A, p' B and p’
C.

76. Three point problem

«These lines may not pass
through the plotted positions a,

b and c since the orientation is
not exact.

A B
8 ?
y /
‘ ‘
\ Cr
«Loosen the tracing paper anc \ E
rotate it so that the rays pas:
through respective points a, k
and c.

+ Now prick the point p' to get the
plotted position ‘p’ of the statior
P.

77. Three point problem: Graphical Method

* Several graphical methods are suggested to solve the three-point
problem.

+ However, the Bessel’s solution is the most commonly used method in
practice being the simplest.

+ The Bessel's solution can be described in the following steps :

78. Three point problem: Graphical Method

*The plane table is set up and
levelled at new station O.

+ The alidade is placed along known
line (say ba on the map) and table
is rotated until A is sighted with ‘a’
pointing towards A as shown in
Figure, clamp the table and sight C
with alidade centered on b.

* Draw a line x-x along alidade edge.

79. Three point problem: Graphical Method

«The alidade is now placed
along ab and table turned
to bisect B with b towards B
as in Figure.

+ Clamp the table and centre
the alidade at a, bisect C by
drawing the ray ac
intersecting the previously
drawn ray x-x at point c’

«Join cc’.

80. Three point problem: Graphical Method

*Alidade is now placed
along c'c as in Figure and
table turned till C is
bisected and clamped in
new position.

«The table is correctly
oriented.

81. Three point problem: Graphical Method

«The alidade is centered at b Me B RE
and Bis bisected. i?

+ Draw the ray to intersect cc’
ino.

+ Similarly, if alidade is pivoted
about a and A is sighted, the
ray will pass through o if the
process is accurate.

82. Three point problem: Trial and Error method or Lehmann’s Method

«In three point problem, if A
the orientation of the plane

table is not proper, the
intersection of the
resectors through the three

points will not meet at a

point but will form a
triangle, known as triangle
of error. Taare a orn
! X

83. Trial & error method

+ Let A,B, & C - three well
defined points.

+ They are plotted on drawing A
sheet as a, b, & c respectively

* It is required to establish station
“o” on the drawing sheet

* Plane table is set up at “O” and
levelled. triana o \
riangle error
IA

* Orientation is done by compass
or by eye judgment

84. «With alidade touching a, b, € c
respectively draw rays Aa, Bb, Cc

« This rays will not pass through one
point , but will form a small triangle
known as “triangle of error”

* This triangle is removed by trial and
error method by rotating plane table
in clockwise and anticlockwise so
that Aa , Bb , Cc pass through one Tiende ol N
i error
point angle X

* This point is the required point and
transfer it on ground as “O” by U
fork and plumb bob.

85. | RESECTION METHOD INTERSECTION METHOD

It isa method of locating station position. It is a method of locating object position

Location of station point is done by occupying station it self Location of object point is done by already plotted
position of station.

For the location of station point back rays are drawn from For the location of object points forward rays are
object points. drawn from station points

It is used when new station of plane table is requied to It is used when it is not possible to measure distance
establish during survey. between station and object points on ground

Can be done by two point problem or three point problem. Can be done by intersection only

Used for large scale work in flate area. Used for small scale survey work in hilly area.

a
2
7

E

Station P