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Unit 3:Unit 3:Compass surveyCompass survey
Unit 5: Compass traversing & Traverse computation
2
Topics covered – Compass Topics covered – Compass SurveyingSurveying
Meridian & Bearing - true, magnetic and arbitrary
Traverse - closed, open.
System of bearing - whole circle bearing, Reduced bearing, fore bearing, and back bearing, conversion from one system to another. Angles from the bearing and vice versa.
Prismatic, Surveyor, Silva and Bronton (introduction) compass
Local attraction with numerical problems.
Plotting of compass survey (Parallel meridian method in detail).
Unit 5: Compass traversing & Traverse computation
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DefinitionDefinition
Limitation of chain surveying
Angle or direction measurement must
Azimuth, Bearing, interior angle, exterior angle, deflection angle
C
B
A
220 L
250 R
B
CA
θ
ß
1800 + θ-ß
CB
A
ßΦED
γ
α
θ
C
B
A
ßΦ
E
D
γα
θ
Unit 5: Compass traversing & Traverse computation
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Compass surveyingCompass surveying
Compass used for measurement of direction of lines
Precision obtained from compass is very limited
Used for preliminary surveys, rough surveying
Unit 5: Compass traversing & Traverse computation
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5.1 Meridian, Bearing & Azimuths5.1 Meridian, Bearing & Azimuths
Meridian: some reference direction based on which direction of line is measured True meridian ( Constant) Magnetic meridian ( Changing) Arbitrary meridian
Source: www.cyberphysics.pwp.blueyonder.co.uk
Bearing: Horizontal angle between the meridian and one of the extremities of line
True bearing Magnetic bearing Arbitrary bearing
Unit 5: Compass traversing & Traverse computation
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5.1 Meridian, Bearing & Azimuths5.1 Meridian, Bearing & Azimuths
True meridian Line passing through geographic north
and south pole and observer’s position Position is fixed Established by astronomical
observations Used for large extent and accurate
survey (land boundary)
Observer’s position
Geographic north pole
Geographic north pole
Contd…
Unit 5: Compass traversing & Traverse computation
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5.1 Meridian, Bearing & Azimuths5.1 Meridian, Bearing & Azimuths
Magnetic meridian Line passing through the direction shown by freely
suspended magnetic needle Affected by many things i.e. magnetic substances Position varies with time (why? not found yet)
Contd…
Assumed meridian Line passing through the direction towards some
permanent point of reference Used for survey of limited extent Disadvantage
Meridian can’t be re-established if points lost.
Unit 5: Compass traversing & Traverse computation
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Reduced bearingReduced bearing
Either from north or south either clockwise or anticlockwise as per convenience
Value doesn’t exceed 900
Denoted as N ΦE or S Φ W
The system of measuring this bearing is known as Reduced Bearing System (RB System)
B
A
SΦW S
W E
N
A
BNΦEN
S
EW
Unit 5: Compass traversing & Traverse computation
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Whole circle bearing (Azimuth) Whole circle bearing (Azimuth)
Always clockwise either from north or south end
Mostly from north end
Value varies from 00 – 3600
The system of measuring this bearing is known as Whole Circle Bearing System (WCB System) B
A
S
W E
N
3000
B
A
S
W E
N450
Unit 5: Compass traversing & Traverse computation
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5.2 Conversion from one system to 5.2 Conversion from one system to otherother
Conversion of W.C.B. into R.B.
S
W E
N
o
Φ
B
θ A
ß
D
αC
Line W.C.B. between Rule for R.B. Quadrants
OAOBOCOD
00 and 900
900 and 1800
1800 and 2700
2700 and 3600
R.B. = W.C.B. = θR.B. = 1800 – W.C.B. = 1800 – ΦR.B. = W.C.B. – 1800 = α – 1800
R.B. = 3600- W.C.B. = 3600- ß.
NθESΦESαESßE
Unit 5: Compass traversing & Traverse computation
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5.2 Conversion from one system to 5.2 Conversion from one system to otherother
Conversion of R.B. into W.C.B.
S
W E
N
o
θß
αΦ
B
AD
C
Line R.B. Rule for W.C.B. W.C.B. betweenOAOBOCOD
NθESΦESαESßE
W.C.B. = R.B.W.C.B. = 1800 – R.B.W.C.B. = 1800 + R.B.W.C.B. = 3600- R.B.
00 and 900
900 and 1800
1800 and 2700
2700 and 3600
Contd…
Unit 5: Compass traversing & Traverse computation
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5.2 Fore & back bearing5.2 Fore & back bearing
Each survey line has F.B. & B.B.In case of line AB, F.B. is the bearing from A to B B.B. is the bearing from B to A
Relationship between F.B. & B.B. in W.C.B.
θ
1800 + θ ß
ß - 1800
D
CB
A
B.B. = F.B. ± 1800
Use + sign if F.B. < 1800
&
use – sign if F.B.>1 1800
Unit 5: Compass traversing & Traverse computation
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5.2 Fore & back bearing5.2 Fore & back bearing
Relationship between F.B. & B.B. in R.B. system
Contd…
NßW
D
C
B
A
SΦWNΦE
SßE
B.B.=F.B.Magnitude is same just the sign changes i.e. cardinal points changes to opposite.
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of angles from 5.2 Calculation of angles from bearing and bearing and vice versa vice versa
In W.C.B.system ( Angle from bearing) Easy & no mistake when diagram is drawn Use of relationship between F.B. & B.B. Knowledge of basic geometry
B
CA
Θ-1800 -ß θ
ß
1800 + θ-ß
ß
θC
A
B
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of angles from 5.2 Calculation of angles from bearing andbearing and vice versa vice versa
In R.B. system (Angle from Bearing) Easy & no mistake when diagram is drawn Knowledge of basic geometry
C
A
B
NθE
SßE
1800-(θ+ß)
Contd…
B
CA
SßESθW
Θ+ß
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of bearing from 5.2 Calculation of bearing from angle angle
Normally in traverse, included angles are measured if that has to be plotted by co-ordinate methods, we need to know the bearing of line Bearing of one line must be measured Play with the basic geometry Diagram is your good friend always
??
?
? Ø
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of bearing from 5.2 Calculation of bearing from angle angle
=?
Contd…
Bearing of line AB = θ1 Back Bearing of line AB = 1800 + θ1
Fore Bearing of line BC =θ2 = α – = α -[3600 –(1800 + θ1) ] = α+ θ1- 1800
= 3600 – BB of line AB = 3600 -(1800 + θ1)
is also = alternate angle of (1800 – θ1) = (1800 – θ1)
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of bearing from 5.2 Calculation of bearing from angle angle
=?
Bearing of line BC = θ2
Back Bearing of line BC = 1800 + θ2
Fore Bearing of line CD = θ3 = ß – = ß -[3600 –(1800 + θ2) ] = ß+ θ2- 1800
= 3600 – BB of line BC = 3600 -(1800 + θ2)
Contd…
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of bearing from 5.2 Calculation of bearing from angle angle
Contd…
?Bearing of line CD= θ3
Back Bearing of line CD = 1800 + θ3
Fore Bearing of line DE = θ4 = γ – = γ -[3600 –(1800 + θ3) ] = γ+ θ3- 1800
= 3600 – BB of line CD = 3600 -(1800 + θ3)
?
Ø
Unit 5: Compass traversing & Traverse computation
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5.2 Calculation of bearing from 5.2 Calculation of bearing from angleangle
Contd…
Ø=?
Bearing of line DE= θ4
Back Bearing of line DE = 1800 + θ4
Fore Bearing of line EF = θ5 = BB of line DE + Ø = 1800 + θ4 + Ø
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
What would be the bearing of line FG if the following angles and bearing of line AB were observed as follows: (Angles were observed in clockwise direction in traverse)
EFG =
DEF =
CDE =
BCD =
ABC =
1240 15’
2150 45’
950 15’1020 00’1560 30’
Bearing of line AB = 2410 30’
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
EFG =
DEF =
CDE =
BCD =
ABC =
1240 15’
2150 45’
950 15’1020 00’1560 30’
Bearing of line AB = 2410 30’
A
2410 30’
B
1240 15’
C
1560 30’
D
1020 00’
E950 15’
F
G
2150 45’
?
A
2410 30’
B
1240 15’
1560 30’
D
1020 00’E
950 15’
F
G
2150 45’
C
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
1240 15’
A
2410 30’
B
FB of line BC = (2410 30’- 1800) + 1240 15’ = 1850 45’
FB of line CD = (1850 45’- 1800) + 1560 30’ = 1620 15’
C
B
1850 45’
C
1560 30’
D
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
FB of line DE =1020 00’ - (1800- 1620 15’) = 840 15’
FB of line EF = (840 15’+1800) + 950 15’ = 3590 30’
C
1620 15’
D
1020 00’E
D
840 15’E
950 15’
F
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
FB of line FG =2150 45’ - {1800+(BB of line EF)}
E
3590 30’
F
G
2150 45’
FB of line FG =2150 45’ - {(1800 +(00 30’)} = 350 15’
A
2410 30’
B
1240 15’
1560 30’
D
1020 00’E
950 15’
F
G
2150 45’
C
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
From the given data, compute the missing bearings of lines in closed traverse ABCD.
A =
810 16’
Bearing of line CD = N270 50’E
Bearing of line AB = ?
Bearing of line AB = ?
360 42’B = D
C
B
A
Bearing of line BC = ?
2260 31’D =
Contd…
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
For the figure shown, compute the following. The deflection angle at B The bearing of CD The north azimuth of DE The interior angle at E The interior angle at F
CN 410 07’E
790 16’A
B
D
EF
S55 0 26’E
S120 47’E
S860 48’W
N120 58’W
Contd…
Unit 5: Compass traversing & Traverse computation
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5.2 Numerical on angle & bearing5.2 Numerical on angle & bearing
CN 410 07’E
790 16’A
B
D
EF
S55 0 26’E
S12 0 47’E
S860 48’W
N12
0 5
8’W
Contd…
Deflection Angle at B = 1800 - (410 07’+550 26’)
= 830 27’ R
Bearing of line CD = 1800 - (790 16’+550 26’)
= S450 18’ W
North Azimuth of line DE = 1800 - 120 47’
= 1670 13’
Interior Angle E = 1800 – (120 47’ + 860 48’)
= 800 25’
Interior Angle F = (120 58’ + 860 48’)
= 990 46’
Unit 5: Compass traversing & Traverse computation
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5.4 Error in compass survey (Local 5.4 Error in compass survey (Local attraction & observational error) attraction & observational error)
Local attraction is the influence that prevents magnetic needle pointing to magnetic north pole
Unavoidable substance that affect are Magnetic ore Underground iron pipes High voltage transmission line Electric pole etc.
Influence caused by avoidable magnetic substance doesn’t come under local attraction such as instrument, watch wrist, key etc
Unit 5: Compass traversing & Traverse computation
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5.4 Local attractions5.4 Local attractions
Let Station A be affected by local attraction
Observed bearing of AB = θ1
Computed angle B = 1800 + θ – ß would not be right.
B
CA
ß
θ1
θ
Unit 5: Compass traversing & Traverse computation
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5.4 Local attractions5.4 Local attractions
Detection of Local attraction By observing the both bearings of line (F.B. & B.B.) and noting
the difference (1800 in case of W.C.B. & equal magnitude in case of R.B.)
We confirm the local attraction only if the difference is not due to observational errors.
If detected, that has to be eliminated
Two methods of elimination First method Second method
Unit 5: Compass traversing & Traverse computation
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5.4 Local attractions5.4 Local attractions
First method Difference of B.B. & F.B. of each lines of traverse is checked to
not if they differ by correctly or not. The one having correct difference means that bearing
measured in those stations are free from local attraction Correction are accordingly applied to rest of station. If none of the lines have correct difference between F.B. &
B.B., the one with minimum error is balanced and repeat the similar procedure.
Diagram is good friend again to solve the numerical problem.
Pls. go through the numerical examples of your text book.
Unit 5: Compass traversing & Traverse computation
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5.4 Local attractions5.4 Local attractions
Second method Based on the fact that the interior angle measured on the
affected station is right. All the interior angles are measured Check of interior angle – sum of interior angles = (2n-4) right
angle, where n is number of traverse side Errors are distributed and bearing of lines are calculated with
the corrected angles from the lines with unaffected station.
Pls. go through the numerical examples of your text book.
Unit 5: Compass traversing & Traverse computation
34
5.5 Traverse, types, compass & 5.5 Traverse, types, compass & chain traversing chain traversing
Traverse A control survey that consists of series of established stations
tied together by angle and distance Angles measured by compass/transits/ theodolites Distances measured by tape/EDM/Stadia/Subtense bar
C
BA
ED
a1
e1
c1
b1
b2
c2
Unit 5: Compass traversing & Traverse computation
35
5.5 Traverse, types, compass & 5.5 Traverse, types, compass & chain traversing chain traversing
Use of traverse Locate details, topographic details Lay out engineering works
Types of Traverse Open Traverse Closed Traverse
C
B
A
ßΦ
E
D
γα
θ
Unit 5: Compass traversing & Traverse computation
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5.5 Types of traverse5.5 Types of traverse
Open traverse Geometrically don’t close No geometric verification Measuring technique must be refined Use – route survey (road, irrigation, coast line etc..)
C
B
A
220 L
250 R
Unit 5: Compass traversing & Traverse computation
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5.55.5
Close traverse Geometrically close (begins and close at same point)-loop traverse Start from the points of known position and ends to the point of
known position – may not geometrically close – connecting traverse Can be geometrically verified Use – boundary survey, lake survey, forest survey etc..
C
B
A
ßΦ
E
D
γα
θ
Types of traverseTypes of traverseContd…
CB
A
220 L
250 R D
Co-ordinate of A &D is already known
Unit 5: Compass traversing & Traverse computation
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5.5 Methods of traversing5.5 Methods of traversing
Methods of traversing Chain traversing (Not chain surveying) Chain & compass traversing (Compass surveying) Transit tape traversing (Theodolite Surveying) Plane-table traversing (Plane Table Surveying)
C
B
A
D
b1b2
a2
a1
c1c2
C
B
A
b2
b1
c2
c1
Aa22 + Aa1
2 - a2a12
cosA2×Aa2×Aa1
=
Unit 5: Compass traversing & Traverse computation
39
5.5 Methods of traversing5.5 Methods of traversing
Chain & compass traversing (Free or loose needle method) Bearing measured by compass &
distance measured by tape/chain Bearing is measured
independently at each station Not accurate as transit – tape
traversing
Contd…
AC
B
D
EF
length
Unit 5: Compass traversing & Traverse computation
40
5.5 Methods of traversing5.5 Methods of traversing
Transit tape traversing Traversing can be done in many ways by transit or
theodolite By observing bearing By observing interior angle By observing exterior angle By observing deflection angle
Contd…
Unit 5: Compass traversing & Traverse computation
41
5.5 Methods of traversing5.5 Methods of traversingContd…
AC
B
D
EF
length
By observing bearing
Unit 5: Compass traversing & Traverse computation
42
5.5 Methods of traversing5.5 Methods of traversingContd…
By observing interior angle Always rotate the theodolite to
clockwise direction as the graduation of cirle increaes to clockwise
Progress of work in anticlockwise direction measures directly interior angle
Bearing of one line must be measured if the traverse is to plot by coordinate method
AE
F
D
CB
length
Unit 5: Compass traversing & Traverse computation
43
5.5 Methods of traversing5.5 Methods of traversingContd…
By observing exterior angle Progress of work in clockwise
direction measures directly exterior angle
Bearing of one line must be measured if the traverse is to plot by coordinate method A
E
F
D
CB
length
Unit 5: Compass traversing & Traverse computation
44
5.5 Methods of traversing5.5 Methods of traversingContd…
By observing deflection angle Angle made by survey line with prolongation of preceding line Should be recorded as right ( R ) or left ( L ) accordingly
CB
A
220 L
250 R D
Unit 5: Compass traversing & Traverse computation
45
5.5 Locating the details in 5.5 Locating the details in traversetraverse
By observing angle and distance from one station
By observing angles from two stations
Unit 5: Compass traversing & Traverse computation
46
5.5 Locating the details in 5.5 Locating the details in traversetraverse
By observing distance from one station and angle from one stationBy observing distances from two points on traverse line
Unit 5: Compass traversing & Traverse computation
47
5.5 Checks in traverse5.5 Checks in traverse
Checks in closed Traverse Errors in traverse is contributed by both angle and distance
measurement Checks are available for angle measurement but There is no check for distance measurement For precise survey, distance is measured twice, reverse
direction second time
Unit 5: Compass traversing & Traverse computation
48
5.5 Checks in traverse5.5 Checks in traverse
Checks for angular error are available Interior angle, sum of interior angles = (2n-4) right angle,
where n is number of traverse side Exterior angle, sum of exterior angles = (2n+4) right angle,
where n is number of traverse side
C
B
A
ßΦ
E
D
γα
θ
Contd…
CB
A
ßΦ
ED
γ
α
θ
Unit 5: Compass traversing & Traverse computation
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5.5 Checks in traverse5.5 Checks in traverse
Deflection angle – algebric sum of the deflection angle should be 00 or 3600.
Bearing – The fore bearing of the last line should be equal to its back bearing ± 1800 measured at the initial station.
C
B
A
ßE
D
θ
ß should be = θ + 1800
Contd…
CB
A
Unit 5: Compass traversing & Traverse computation
50
5.5 Checks in traverse5.5 Checks in traverse
Checks in open traverse No direct check of angular measurement is available Indirect checks
Measure the bearing of line AD from A and bearing of DA from D Take the bearing to prominent points P & Q from consecutive
station and check in plotting.
C
BA
ED
E
C
BA
ED
C
Q
P
D
Contd…
Unit 5: Compass traversing & Traverse computation
51
5.6 Field work and field book5.6 Field work and field book
Field work consists of following stepsSteps Reconnaissance Marking and Fixing survey station First Compass traversing then only detailing Bearing measurement & distance measurement
Bearing verification should be done if possible Details measurement
Offsetting Bearing and distance Bearings from two points Bearing from one points and distance from other point
Unit 5: Compass traversing & Traverse computation
52
5.6 Field work and field book5.6 Field work and field book
Field book Make a sketch of field
with all details and traverse in large size
Line Bearing Distance Remarks
AB
AE
BA
BC
CB
CD
DC
DE
ED
EA
C
B
ED
Ab1
b3b4
b2
w1
w2
Contd…
Line Bearing Distance Remarks
Bw1
Cw2
Db2
Db3
Eb4
Eb1
Unit 5: Compass traversing & Traverse computation
53
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Methods of plotting a traverse Angle and distance method Coordinate method
LAT
ITU
DE
AX
IS
E (74.795, 49.239)D (26.879, 353.448)
C (138.080, 446.580)
B(295.351, 429.986)
A (300.000, 300.000)
DEPARTURE AXIS (0,0)
Unit 5: Compass traversing & Traverse computation
54
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Angle and distance method Suitable for small survey Inferior quality in terms of accuracy of plotting Different methods under this
By protractor By the tangent of angle By the chord of the angle
Contd…
Unit 5: Compass traversing & Traverse computation
55
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
By protractor Ordinary protractor with minimum graduation 10’ or 15’
Contd…
Unit 5: Compass traversing & Traverse computation
56
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
By the tangent of angle Trignometrical method Use the property of right angle triangle, perpendicular
=base × tanθ
θb
P = b× tanθ
BA
D
Contd…
A
B
600
5cm 5cm
×tan60
0 cm
D
Unit 5: Compass traversing & Traverse computation
57
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
By the chord of the angle Geometrical method of laying off an angle
r BA
D
θA
450
5cm
(2×5×sin 450/2)cm
D
B
Contd…
rsinθ/2θ/2
θ/2
Chord r’ = 2rsinθ/2
Unit 5: Compass traversing & Traverse computation
58
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Coordinate method Survey station are plotted by their co-ordinates. Very accurate method of plotting Closing error is balanced prior to plotting-Biggest
advantage
C
BA
D C’
B’A’
D’
E’
E
e’
C
BA
D
E
Contd…
Unit 5: Compass traversing & Traverse computation
59
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverseWhat is co-ordinates Latitude
Co-ordinate length parallel to meridian +ve for northing, -ve for southing Magnitude = length of line× cos(bearing angle)
Departure Co-ordinate length perpendicular to meridian +ve for easting, -ve for westing Magnitude = length of line× sin(bearing angle)
(+,+)
(-,-)
( +,-)
A
θ
B
L =
l×
cosθ
D = l×sinθ
I
(-, +)
IV
III II
l
Contd…
Unit 5: Compass traversing & Traverse computation
60
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Consecutive co-ordinate Co-ordinate of points with reference to preceding point Equals to latitude or departure of line joining the preceding
point and point under consideration If length and bearing of line AB is l and θ, then consecutive
co-ordinates (latitude, departure) is given by Latitude co-ordinate of point B = l×cos θ Departure co-ordinate of point B = l×sin θ
A
θ
B
l
Contd…
Unit 5: Compass traversing & Traverse computation
61
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Total co-ordinate Co-ordinate of points with reference to common origin Equals to algebric sum of latitudes or departures of lines between the
origin and the point The origin is chosen such that two reference axis pass through most
westerly If A is assumed to be origin, total co-ordinates (latitude, departure) of
point D is given by Latitude co-ordinate = (Latitude coordinate of A+ ∑latitude of AB, BC, CD) Departure co-ordinate = (Departure coordinate of A+ ∑Departure of AB,
BC, CD)
C
B
AD
Contd…
Unit 5: Compass traversing & Traverse computation
62
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
For a traverse to be closed Algebric sum of latitude and departure should be zero.
Dep. DA (+)
C
B
A
D
Lat
. D
A(+
)L
at.
AB
(+)Dep. AB (-)Dep. BC (-)
Dep. CDL
at.
CD
(+)
Lat
. B
C(-
)
Contd…
Unit 5: Compass traversing & Traverse computation
63
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Real fact is that there is always error Both angle & distance Traverse never close Error of closure can be
computed mathematically
Closing Error (A’A) =√(∑Lat2+ ∑dep
2 )
Bearing of A’A = tan-1 ∑dep/∑lat
Dep. DA’C
B
A
D
A’
Lat
. D
A’
Lat
. A
BDep. ABDep. BC
Lat
. C
D
Lat
. B
C
Dep. CD
Contd…
∑lat
∑dep
A
A’
θ
Unit 5: Compass traversing & Traverse computation
64
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Error of closure is used to compute the accuracy ratio Accuracy ratio = e/P, where P is perimeter of traverse This fraction is expressed so that numerator is 1 and denominator
is rounded to closest of 100 units. This ratio determines the permissible value of error.
Contd…
S.N. Types of traverse Permissible value of total linear error of closure
4
5
Minor theodolite traverse for detailing
Compass traverse
1 in 3,000
1 in 300 to 1 in 600
Unit 5: Compass traversing & Traverse computation
65
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
What to do if the accuracy ratio is unsatisfactory than that required Double check all computation Double check all field book entries Compute the bearing of error of closure Check any traverse leg with similar bearing (±50) Remeasure the sides of traverse beginning with a
course having a similar bearing to the error of closure
Contd…
Unit 5: Compass traversing & Traverse computation
66
5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Balancing the traverse (Traverse adjustment) Applying the correction to latitude and departure so
that algebric sum is zero
Methods Compass rule (Bowditch)
When both angle and distance are measured with same precision
Transit rule When angle are measured precisely than the length
Graphical method
Contd…
Unit 5: Compass traversing & Traverse computation
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5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Bowditch ruleClat ∑L
∑l
= l× Cdep ∑D
∑l
= l×
Where Clat & Cdep are correction to latitude and departure
∑L = Algebric sum of latitude
∑D = Algebric sum of departure
l = length of traverse leg
∑l = Perimeter of traverse
Transit rule
Clat ∑L
LT
= L× Cdep ∑D
∑DT
= D×
Where Clat & Cdep are correction to latitude and departure
∑L = Algebric sum of latitude
∑D = Algebric sum of departure
L = Latitude of traverse leg
LT = Arithmetic sum of Latitude
Contd…
Unit 5: Compass traversing & Traverse computation
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5.7 Computation & plotting 5.7 Computation & plotting a traverse a traverse
Graphical rule Used for rough survey Graphical version of
bowditch rule without numerical computation
Geometric closure should be satisfied before this.
C
BA
D C’
B’A’
D’
E’
E
e’
A C’B’ A’D’ E’
e’
aedcb
Contd…
Unit 5: Compass traversing & Traverse computation
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5.7 Example of coordinate 5.7 Example of coordinate methodmethod
Plot the following compass traverse by coordinate method in scale of 1cm = 20 m.
Line Length (m) Bearing
AB 130.00 S 880 E
BC 158.00 S 060 E
CD 145.00 S 400 W
DE 308.00 N 810 W
EA 337.00 N 480 E
E
B
C
D
A
Unit 5: Compass traversing & Traverse computation
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5.7 Example of coordinate 5.7 Example of coordinate methodmethod
Step 1: calculate the latitude & departure coordinate length of survey line and value of closing error
Line Bearing Length (m) Latitude co ordinate Departure Coordinate
AB
BC
CD
DE
EA
S 880 E
S 060 E
S 400 W
N 810 W
N 480 E
130.00
158.00
145.00
308.00
337.00
-4.537
-157.134
-111.076
48.182
225.497
129.921
16.515
-93.204
-304.208
250.440
∑L= 0.932 ∑D = - 0.536
Closing Error (e) =√ (∑L2+ ∑D2 )
Closing Error (e) = 1.675 m
P = ∑l = 1078.00 m
Unit 5: Compass traversing & Traverse computation
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5.7 Example of coordinate 5.7 Example of coordinate methodmethod
Step 2: calculate the ratio of error of closure and total perimeter of traverse (Precision)Precision = e/P = 1.675/1078 = 1/643 which is okey with reference to permissible value (1 in 300 to 1 in 600)
Step 3: Calculate the correction for the latitude and departure by Bowditch’s method
Clat(AB) 0.932
1078
= 130×
= - 0.112
Cdep(AB) 0.536
1078
= 130×
= + 0.065
Unit 5: Compass traversing & Traverse computation
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5.7 Example of coordinate 5.7 Example of coordinate methodmethod
Step 4: Apply the correction worked out (balancing the traverse)
Line Latitude coordinate
Departure coordinate
Correction to Latitude
Correction to Departure
Corrected Latitude
co ordinate
Corrected Departure Coordinate
AB
BC
CD
DE
EA
-4.537
-157.134
-111.076
48.182
225.497
129.921
16.515
-93.204
-304.208
250.440
-0.112
-0.137
-0.125
-0.226
-0.291
+0.065
+0.079
+0.072
+0.153
+0.168
- 4.649
- 157.271
- 111.201
+ 47.916
+225.206
+129.986
+ 16.594
- 93.132
- 304.055
+ 250.608
∑L= 0 ∑D = 0
Unit 5: Compass traversing & Traverse computation
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5.7 Example of coordinate 5.7 Example of coordinate methodmethod
Step 5: Calculate the total coordinate of stations
Line Corrected Latitude
co ordinate
Corrected Departure Coordinate
Stations Total Latitude Coordinate
Total Departure Coordinate
AB
BC
CD
DE
EA
- 4.649
- 157.271
- 111.201
+ 47.916
+ 225.206
+129.986
+ 16.594
- 93.132
-304.055
+ 250.608
A
B
C
D
E
A
300.000
(assumed)
295.351
138.080
26.879
74.795
300.000 (CHECK)
300.000
(assumed)
429.986
446.580
353.448
49.239
300.00(CHECK)
Unit 5: Compass traversing & Traverse computation
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5.7 Example of coordinate 5.7 Example of coordinate methodmethod
E (74.795, 49.239)D (26.879, 353.448)
C (138.080, 446.580)
B(295.351, 429.986)
A (300.000, 300.000)
LAT
ITU
DE
AX
IS
DEPARTURE AXIS (0,0)
Unit 5: Compass traversing & Traverse computation
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Degree of accuracy in Degree of accuracy in traversingtraversing
The angular error of closure in traverse is expressed as equal to C√N Where C varies from 15” to 1’ and N is the number of angle
measured
S.N. Types of traverse Angular error of closure
Total linear error of closure
1
2
3
4
5
First order traverse for horizontal control
Second order traverse for horizontal control
Third order traverse for survey of important boundaries
Minor theodolite traverse for detailing
Compass traverse
6”√N
15”√N
30”√N
1’N
15’√N
1 in 25,000
1 in 10,000
1 in 5,000
1 in 3,000
1 in 300 to 1 in 600
Unit 5: Compass traversing & Traverse computation
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5.7 Tutorial5.7 Tutorial
Plot the traverse by co-ordinate method, where observed data are as followsInterior anglesA = 1010 24’ 12” B = 1490 13’ 12” C = 800 58’ 42” D = 1160 19’ 12” E = 920 04’ 42”
Side lengthAB = 401.58’, BC = 382.20’, CD = 368.28’DE = 579.03’, EA = 350.10’Bearing of side AB = N 510 22’ 00” E (Allowable precision is 1/3000)
E
B C
DA
Unit 5: Compass traversing & Traverse computation
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