Traverse Surveying
>
Traversing is the type of survey in which number of connected survey lines
forms the framework.
> The directions ofthese
survey lines are measured with any angle (direction) measuring
instrument such as compass, theodolite, etc. and
lengths of survey lines are measured by chain or tape.
> When
starting point and end point ofthis framework meets at the end of survey, then
it is known as closed traverse.
Example: lakes, buildings, large
areas, etc.
> When framework ends somewhere else it is known as
open traverse
Example: roads canals and coast
line survey.
Methods of traversing:
Arc based on instruments used in
determining the relative directions ofthe traverse lines.
1)
Chain traversing:
> Whole work is done with the
help of chain and tape only.
2)
Chain and compass traversing (loose or free needle
method)
> Lengths of lines are measured with chain or tape
and bearings are measured with compass. > Both FB and BB are taken at each
station.
> Magnetic meridian is established at each station.
\
3)
Transit type traversing:
a)
By fast needle method.
b)
By measurement of angles between the lines.
a)
By fast needle method
> Magnetic bearings are
measured with theodolite fitted with compass.
>
Magnetic meridian is established only at first station and direction of lines
are measured with reference to magnetic meridian established at first station.
> More accurate than loose
needle method. Since, least count of theodolite is less then compass. >
Compass is used only to fix meridian direction, angles are measured by using
theodolite only.
b)
By measurement of angles between the lines:
> Angles are measured directly
by using theodolite and frame work is constructed.
> Most accurate method than
all previous methods.
Checks in traverse
survey:
Traversing involves two types of
errors i.e. linear and angular error.
> Check for linear error:
(closed and open traverse)
Linear error i.e. error in measuring
length can be rectified by measuring length second time,
preferably in reverse direction
on different dates by different parties.
> Checks for angular error
(closed traverse)
1)
Traverse by included angles.
Sum of measured interior angles
=(2N - 4) × right angle
- If exterior angles are measured,
Sum of measured exterior angles =
(2N + 4) × right angle.
Where N = number of sides of
traverse.
2)
Traverse by deflection angles
The algebraic sum of deflection angles should be equal
to 3600, taking the right hand deflection angles positive and left
hand deflection angles as negative.
3)
Traverse by direct observation of bearings
FB of last line = BB of last
line 1800 measured at the initial station.
Checks in open
traverse:
No direct check for angular
measurement is available. But indirect checks can be made as
follows.
Similarly bearing ofDA
Can be measured and
corresponding check can be applied.
Plotting of Traverse
Survey:
There are two main methods
ofplotting a traverse survey:
1) Angle and distance method,
2) Co-ordinate method.
1) Angle and distance method:
> In this
method, distances between stations are laid off to scale and angles
(bearings)are plotted by one ofthe following method.
>
Method is suitable for small survey works and much inferior than co-ordinate
method in terms of accuracy ofplotting.
More commonly used angle plotting
methods are
a)
By protractor
b)
By tangent method (trigonometric method)
- In a right angle triangle
Perpendicular = bade x tan θ
c)
Chord method (geometric method)
- To plot angle θ draw an arc with O as centre and any
radius chord bd = 2r sin (θ/2). With b as centre draw an arc of length bd. join
O and d u will get angle θ
2) Co-ordinate method.
> In this method, survey
stations are plotted by calculating their co-ordinates.
> Most practical and accurate
method ofplotting traverses.
> The biggest advantages are
that the closing error can be eliminated by balancing prior to
plotting.
> There are two methods of calculating
co-ordinates.
a)
Dependent or consecutive co-ordinates,
b)
Independent co-ordinates.
a) Dependent or consecutive
co-ordinates:
Latitude (L):
> Latitude of a survey line is
its co-ordinate length measured parallel to an assumed meridian
direction. (i.e. true north or
magnetic north or any assumed meridian).
> Latitude is positive when
measured upward (or northward) and is called as northing. Similarly it
is negative when measured
downward (or southward) and is called as southing.
Departure (D):
> Departure of a survey line
is its co-ordinate length measured perpendicular to reference
meridian direction.
> Departure is positive when measured eastward and
is termed as easting.
It is negative when measured
westward and is called as westing.
Latitude is a projection of
survey line on N-S direction. (Assumed meridian direction)
Departure is a projection of survey line on E-W direction (direction 1lar
to meridian)
|
Line
|
WCB
|
RB
|
Latitude
|
Departure
|
|
OA
|
0 - 900
|
NOE
|
+
|
+
|
|
OB
|
900 -
1800
|
SOE
|
-
|
+
|
|
OC
|
1800 -
2700
|
SOW
|
-
|
-
|
|
OD
|
2700 -
3600
|
NOW
|
+
|
-
|
> Latitude and departure of any point
therefore with reference to the preceding point are equal to the latitude and
departure of line joining point under consideration and preceding point. Such
co-ordinates are called as consecutive or dependent co-ordinate.
b) Independent co-ordinates:
> Coordinates of any traverse
stations can be calculated with respect to a common origin.
> When total latitude and departure of all
stations is calculated with respect to common origin then these coordinates are
called as independent or total co-ordinates ofa traverse station.
>
Total co-ordinates for any
point can be calculated by adding algebraically latitudes and departures
oflines between that point and common origin.
Total latitude (or departure) of
end point of a traverse = total latitudes (or departures) of first
point oftraverse plus algebraic
sum of all the latitudes (or departures).
Independent coordinate of A = (L1,
D1)
Independent coordinate of B = (L1
– L2, D1+D2)
Independent coordinate of C = (L1
– L2 – L3, D1 + D2 – D3)
Independent coordinate of O = (L1
– L2 – L3 – L4, D1 + D2
– D3 – D4)
Closing error:
> If a closed traverse is plotted
according to field measurements then the end point and starting
point oftraverse will not meet.
Due to errors in field measurements of angles and distances such
error is called as “closing
error”
> In a closed traverse, L =0
& D =0 otherwise there is a closing error.
> The error of closure can be
determined by finding L & D , both these are the component
of error e parallel and
perpendicular to meridian respectively.
2 2
> Thus
closing error ( ) ( )
e = L + D=AA
> The
direction of closing error is given by,
tan D
L
> The sign of D & L will
define the quadrant in which closing error lies.
Note:
before calculating
latitudes and departures, the traverse angles should be adjusted to satisfy
geometric conditions.
i.e. check for
angular error should be given before calculating latitudes and departures. Adjustment
of bearings:
> Let Q be the closing
error in bearing of last line of a closed traverse having N sider.
correction for first
line = Q
N
correction for second line =
correction for third line = 3Q
N
. . correction
for last line =___ = e.
NQ
N
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