Balancing the
traverse
>
The
term balancing means applying corrections to latitudes and departures so that EL =
0 & ED = 0 . Applicable only for closed traverse.
> Traverse is said to be
balanced when EL = 0 & ED = 0
> Following are the
balancing methods.
1)
Bowditch’s method,
2)
Transit method
3)
Graphical method
4)
Axis method.
1) Bowditch’s method:
(compass rule)
>
Based on the assumption that
errors in linear measurement oc l and errors in angular
Based on the assumption that
errors in linear measurement oc l and errors in angular
1
 |
> Also called as compass
rule.
> Bowditch’s method is used when linear and
angular measurements are of equal precision (importance).
> Bowditch rule is,
Correction to latitude (or departure) ofany side =
total error in latitude (or departure) × length of that side / perimeter of
traverse
l l
C & D
L L____ C D
l l
CL = correction to
latitude of any side.
CD = correction to
departure of any side,
ΣL = total error in latitude,
ΣD = total error in departure,
Σ l = length of
perimeter,
l = length of side
under consideration.
2)
Transit method:
>
Used where angular measurements are more precise theodo + chain than the linear
measurements.
> According to this rule total error in latitudes
and in departures is distributed in proportion to the latitudes and departures
of the sides.
> Angles are less affected when corrections applied
by transit method than by Bowditch method. > Transit rule is,
Correction to latitude (or departure) of any side =
total error in latitude (or departure) x latitude (or departure) of that line/
arithmetic sum oflatitudes (or departures).
L D
C & C
L L D
D
L D
T T
Where,
L, D – latitude and departure of
line respectively,
LT-, DT –
arithmetic sum of latitude and departure respectively.
3)
Graphical method:
> For rough survey, such as
compass traverse survey, the Bowditch’s rule is applied graphically
without doing theoretical
calculations.
> No need to calculate
latitudes and departures
4)
Axis
method:
> Used when angles are
measured very accurately, the corrections are applied to lengths only. >
Directions of the lines are unchanged. Thus the general shape ofthe diagram is
preserved.
 |
length of axis
> Degree of accuracy in traversing
depends upon the type of instruments used for linear and
angular measurements and also
upon the purpose and extent of survey.
> The degree ofprecision
(accuracy) used in angular measurements must be consistent with the
degree of precision used in
linear measurements so that the effect of error in angular
measurement will be the same as
that of error in linear measurement.
Let D be the correct position of
point w. r. to a point A such that AD = l and angle of BAD=0.
In the field measurement let SO
be the error in angular measurement and e be the error in linear
measurement so that D2 is the
faulty position ofpoint D.
Now,
Displacement of D due to angular
error (SQ) = DD1 =l tan SO
Displacement of D due to linear
error = D1 D2 = e.
In order to have same degree of
precision in the two measurements.
l tan sO = e.
SO = tan-'(e/l)
e/l = ratio of linear
error.
Omitted Measurements:
> Generally in traverse survey
length and direction of each survey line is measured in the field
> However sometimes it is not
possible to take all measurements due to obstacles or because of
oversight, called as omitted
measurements or missing quantities.
>
Such omitted measurements can
be calculated by latitudes and departures provided quantities required are not
more than two.
> For a closed traverse L =0 & D =0.
L = l 1
cosO 1 + 2cosO2 +l3
cosO3 +.......
D = l 1
sinO 1 + 2sinO2 +l3
sinO3 +....... There are
four general cases of omitted.
I)
When
the bearing of one side is omitted. When the length of one side is omitted.
When the bearing and length of one side is omitted.
II)
When the bearing of one side and length of another side
is omitted.
III) When the lengths of two
sides are omitted.
IV)
When
the bearings oftwo sides are omitted. Gales traverse table:
-
Traverse computations are usually done in tabular form, a more common form
being gales Traverse table.
- Useful for both dependent and independent
co-ordinates.
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