TRAVERSE in land surveying and technique
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Apr 28, 2024
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About This Presentation
Tranverse psychology
Slide Content
Traverse Computations
In Civil Works
In Civil Works
2
Traverse
A traverse is a series of consecutive lines
whose ends have been marked in the field,
and whose lengths and directions have
been determined from measurements
►Used to locate topographic details for
the preparation of plans
►To lay out (setting-out) or locate
engineering works
Traverse
A traverse is a series of consecutive lines
whose ends have been marked in the field,
and whose lengths and directions have
been determined from measurements
►Used to locate topographic details for
the preparation of plans
►To lay out (setting-out) or locate
engineering works
Two types
Close
Open
Main applications of traversing
Establishing coordinates for new points
(E,N)
new
(E,N)
new
(E,N)
known
(E,N)
known
(E,N)
known
(E,N)
known
Close
Open
Main applications of traversing
Establishing coordinates for new points
(E,N)
new
(E,N)
new
(E,N)
known
(E,N)
known
(E,N)
known
(E,N)
known
4
Closed traverse
Closed traverse can be link or polygon
Polygon (loop)
The lines returns to the starting point, thus
forming a closed figure
Geometrically and mathematically closed
Link
Begins and ends at points whose positions have
been previously determined
Geometrically open, mathematically closed
Closed traverse
Closed traverse can be link or polygon
Polygon (loop)
The lines returns to the starting point, thus
forming a closed figure
Geometrically and mathematically closed
Link
Begins and ends at points whose positions have
been previously determined
Geometrically open, mathematically closed
5
Open traverse
Series of measured lines and angles that do
not return to the starting point or close upon
a previously determined point.
Geometrically and mathematically open
Lack of geometrical closure means no
geometrical verification of actual positions of
traverse stations
No means of checking for observational
errors and mistakes
Should be avoided
Open traverse
Series of measured lines and angles that do
not return to the starting point or close upon
a previously determined point.
Geometrically and mathematically open
Lack of geometrical closure means no
geometrical verification of actual positions of
traverse stations
No means of checking for observational
errors and mistakes
Should be avoided
6
What is a traverse?
A closed
traverse
A traverse between
known points
Loop
Link
What is a traverse?
A closed
traverse
A traverse between
known points
Loop
Link
7
Traverse computation
Traverse computations are concerned with
deriving co-ordinates for the new points
that were measured, along with some
quantifiable measure for the accuracy of
these positions.
The co-ordinate system most commonly
used is a grid based rectangular orthogonal
system of eastings (X) and northings (Y).
Traverse computations are cumulative in
nature, starting from a fixed point or known
line, and all of the other directions or
positions determined from this reference.
Traverse computation
Traverse computations are concerned with
deriving co-ordinates for the new points
that were measured, along with some
quantifiable measure for the accuracy of
these positions.
The co-ordinate system most commonly
used is a grid based rectangular orthogonal
system of eastings (X) and northings (Y).
Traverse computations are cumulative in
nature, starting from a fixed point or known
line, and all of the other directions or
positions determined from this reference.
8
Choosing location of traverse stations
1.Minimize # of stations (each line of sight: as
long as possible)
2.Ensure: adjacent stations always inter-visible
3.Avoid acute traverse angles
4.Stable & safe ground conditions for instrument
5.Marked with paint or/and nail; to survive
subsequent traffic, construction, weather
conditions, etc.
Choosing location of traverse stations
1.Minimize # of stations (each line of sight: as
long as possible)
2.Ensure: adjacent stations always inter-visible
3.Avoid acute traverse angles
4.Stable & safe ground conditions for instrument
5.Marked with paint or/and nail; to survive
subsequent traffic, construction, weather
conditions, etc.
9
6.Include existing stations / reference objects
for checking with known values
7.Traverse must not cross itself
8.Network formed by stations (if any): as
simple as possible
9.Do the above without sacrificing accuracy or
omitting important details
Choosing location of traverse stations
6.Include existing stations / reference objects
for checking with known values
7.Traverse must not cross itself
8.Network formed by stations (if any): as
simple as possible
9.Do the above without sacrificing accuracy or
omitting important details
Choosing location of traverse stations
Datum check
Check if the opening and closing control
points are in-situ
Measure distance between and check the
direction by compass/or a theodolite
Compute the distance and bearings by
join computation
Compare the results [should be within
limits]
10
Check if the opening and closing control
points are in-situ
Measure distance between and check the
direction by compass/or a theodolite
Compute the distance and bearings by
join computation
Compare the results [should be within
limits]
10
Join computation
UT249251423.671522931.693
UT239251325.691522838.060
CHANGE -97.980 -93.633
11
UT249251423.671522931.693
UT239251325.691522838.060
CHANGE -97.980 -93.633
11
12
TraverseComputation
1)Calculation of startingand closingbearings;
2)Calculation of angular misclosureby
comparing the sum of the observed bearings
with the closing bearings.
3)If angular misclosure is acceptable,
distributeit throughout the traverse in equal
amountsto each angle.
4)Reduction of slope distanceto horizontal
distance;
TraverseComputation
1)Calculation of startingand closingbearings;
2)Calculation of angular misclosureby
comparing the sum of the observed bearings
with the closing bearings.
3)If angular misclosure is acceptable,
distributeit throughout the traverse in equal
amountsto each angle.
4)Reduction of slope distanceto horizontal
distance;
13
Traverse Computation (con’t)
5)Calculation of the changes in coordinates
(N, E) of each traverse line.
6)Assessing the coordinate misclosure.
7)Balancing the traverse by distributing the
coordinate misclosure throughout the
traverse lines.
8)Computation of the final coordinates of each
point relative to the starting station, using
the balanced values of N, E per line.
Traverse Computation (con’t)
5)Calculation of the changes in coordinates
(N, E) of each traverse line.
6)Assessing the coordinate misclosure.
7)Balancing the traverse by distributing the
coordinate misclosure throughout the
traverse lines.
8)Computation of the final coordinates of each
point relative to the starting station, using
the balanced values of N, E per line.
14
Angular misclosure
The numerical diff. between the existing
bearing and the measured one is called
the angular misclosure.
There is usually a permissible limit for
this misclosure, depending upon the
accuracy requirements and
specifications of the survey.
Angular misclosure
The numerical diff. between the existing
bearing and the measured one is called
the angular misclosure.
There is usually a permissible limit for
this misclosure, depending upon the
accuracy requirements and
specifications of the survey.
Angular misclosure
A typical computation for the allowable
misclosure is given by = kn
where n is the number of angles
measured and k is a fraction based on
the least division of the theodolite
scale.
E.g, if k is 1”, for a traverse with 10
measured angles, the allowable
misclosure is 3.1623”.
15
A typical computation for the allowable
misclosure is given by = kn
where n is the number of angles
measured and k is a fraction based on
the least division of the theodolite
scale.
E.g, if k is 1”, for a traverse with 10
measured angles, the allowable
misclosure is 3.1623”.
15
Angular misclosure
For a closed link traverse, the check is
given by
A
1
+(angles) –A
2
= (n –1) 180
where A
1
is the initial or starting
bearing, A
2
is the closing or final
bearing, and nis the number of
angles measured.
16
For a closed link traverse, the check is
given by
A
1
+(angles) –A
2
= (n –1) 180
where A
1
is the initial or starting
bearing, A
2
is the closing or final
bearing, and nis the number of
angles measured.
16
17
Angular misclosure
Once the traverse angles are within
allowable range, the remaining misclosure
is distributed amongst the angles.
This process is called balancing the angles
as follows
Average adjustment
Misclosure is divided by number of angles and
correction inserted into all of the angles.
Most common technique
Angular misclosure
Once the traverse angles are within
allowable range, the remaining misclosure
is distributed amongst the angles.
This process is called balancing the angles
as follows
Average adjustment
Misclosure is divided by number of angles and
correction inserted into all of the angles.
Most common technique
18
Angular misclosure
Arbitrary adjustment
if misclosure is small, then it may be inserted
into any angle arbitrarily (usually one that may
be suspect).
If no angle suspect, then it can be inserted into
more than one angle.
Adjustment based on measuring conditions
If a line has particular obstruction that may have
affected observations, misclosure may be divided
and inserted into the two angles affected.
Angular misclosure
Arbitrary adjustment
if misclosure is small, then it may be inserted
into any angle arbitrarily (usually one that may
be suspect).
If no angle suspect, then it can be inserted into
more than one angle.
Adjustment based on measuring conditions
If a line has particular obstruction that may have
affected observations, misclosure may be divided
and inserted into the two angles affected.
19
Traversing -Computations
Errors in angular measurement are not
related to the size of the angle.
Once the angles have been balanced, they
can be used to compute the bearings of the
lines in the traverse.
Starting from the bearing of the original fixed
control line, the internal or clockwise
measured angles are used to compute the
forward azimuths of the new lines.
The bearing of this line is then used to
compute the bearing of the next line and so
on
Traversing -Computations
Errors in angular measurement are not
related to the size of the angle.
Once the angles have been balanced, they
can be used to compute the bearings of the
lines in the traverse.
Starting from the bearing of the original fixed
control line, the internal or clockwise
measured angles are used to compute the
forward azimuths of the new lines.
The bearing of this line is then used to
compute the bearing of the next line and so
on
20
Misclosure and adjustment
For closed traverses, co-ordinates of the final
ending station are known, this provides a
mathematical check.
If the final computed E and N are compared
to the known E and N for the closing station,
then co-ordinate misclosures can be
determined.
The E misclosure E is given by
dE = final computed E –final known E
similarly, the N misclosure N is given by
dN = final computed N –final known N
Misclosure and adjustment
For closed traverses, co-ordinates of the final
ending station are known, this provides a
mathematical check.
If the final computed E and N are compared
to the known E and N for the closing station,
then co-ordinate misclosures can be
determined.
The E misclosure E is given by
dE = final computed E –final known E
similarly, the N misclosure N is given by
dN = final computed N –final known N
21
Linear Misclosure of Traverse22
dE dN
dE = error in easting of last station (= observed -known)
dN = error in northing of last station (= observed -known)
Fractional accuracy:f
L
Order Max
Max f Typical survey task
First 1 in 25000Control or monitoring surveys
Second 1 in 10000Engineering Surveying;
Setting out surveys
Third 1 in 50002n 10n 30n
Linear Misclosure of Traverse22
dE dN
dE = error in easting of last station (= observed -known)
dN = error in northing of last station (= observed -known)
Fractional accuracy:f
L
Order Max
Max f Typical survey task
First 1 in 25000Control or monitoring surveys
Second 1 in 10000Engineering Surveying;
Setting out surveys
Third 1 in 50002n 10n 30n
22
Example: Traverse Computation (con’t)
Another options
For each leg, calculate N[Dist * cos(Brg)] & E
[Dist * sin(Brg)].
Compute Sum N and Sum E.
Compare results with diff. between start and end
coords.
The difference is dE and dN
Example: Traverse Computation (con’t)
Another options
For each leg, calculate N[Dist * cos(Brg)] & E
[Dist * sin(Brg)].
Compute Sum N and Sum E.
Compare results with diff. between start and end
coords.
The difference is dE and dN
23
Linear Misclosure
•Thesediscrepanciesrepresentthedifferenceonthe
groundbetweenthepositionofthepointcomputedfrom
theobservationsandtheknownpositionofthepoint.
•TheEandNmisclosuresarecombinedtogivethe
linearmisclosureofthetraverse,where
linear misclosure = (E
2
+ N
2
)
E
N
Linear Misclosure
•Thesediscrepanciesrepresentthedifferenceonthe
groundbetweenthepositionofthepointcomputedfrom
theobservationsandtheknownpositionofthepoint.
•TheEandNmisclosuresarecombinedtogivethe
linearmisclosureofthetraverse,where
linear misclosure = (E
2
+ N
2
)
E
N
24
Traversing –Precision
By itself the linear misclosure only gives a
measure of how far the computed position
is from the actual position (accuracy of the
traverse measurements).
Another parameter that is used to provide
an indication of the relative accuracy of
the traverse is the proportional linear
misclosure.
Traversing –Precision
By itself the linear misclosure only gives a
measure of how far the computed position
is from the actual position (accuracy of the
traverse measurements).
Another parameter that is used to provide
an indication of the relative accuracy of
the traverse is the proportional linear
misclosure.
25
Traversing -Computations
If a misclosure exists, then the figure
computed is not mathematically closed.
This can be clearly illustrated with a closed
loop traverse.
The co-ordinates of a traverse are
therefore adjusted for the purpose of
providing a mathematically closed figure
while at the same time yielding the best
estimates for the horizontal positions for
all of the traverse stations.
Traversing -Computations
If a misclosure exists, then the figure
computed is not mathematically closed.
This can be clearly illustrated with a closed
loop traverse.
The co-ordinates of a traverse are
therefore adjusted for the purpose of
providing a mathematically closed figure
while at the same time yielding the best
estimates for the horizontal positions for
all of the traverse stations.
26
Discrepancies between eastings and
northings must be adjusted before
calculating the final coordinates.
Adjustment methods:
Compass Rule
Least Squares Adjustment
Bowditch Rule
Bowditch Rule is most commonly used.
AdjustmentofTraverse
Discrepancies between eastings and
northings must be adjusted before
calculating the final coordinates.
Adjustment methods:
Compass Rule
Least Squares Adjustment
Bowditch Rule
Bowditch Rule is most commonly used.
AdjustmentofTraverse
27
devised by Nathaniel Bowditch in 1807.
AdjustmentbyBowditchRule
Ei, Ni = Coordinate corrections
dE, dN = Coordinate Misclosure (constant)
Li = Sum of the lengths of the traverse (constant)
Li = Horizontal length of the i
th
traverse leg.in
i
i
i L
L
dE
E
1
in
i
i
i
L
L
dN
N
1
devised by Nathaniel Bowditch in 1807.
AdjustmentbyBowditchRule
Ei, Ni = Coordinate corrections
dE, dN = Coordinate Misclosure (constant)
Li = Sum of the lengths of the traverse (constant)
Li = Horizontal length of the i
th
traverse leg.in
i
i
i L
L
dE
E
1
in
i
i
i
L
L
dN
N
1
28
Adjustments -Arbitrary
The arbitrary method is based upon the
surveyor’s individual judgement
considering the measurement conditions.
The Least Squares method is a rigorous
technique that is founded upon
probabilistic theory.
It requires an over-determined solution
(redundant measurements) to compute
the best estimated position for each of the
traverse stations.
Adjustments -Arbitrary
The arbitrary method is based upon the
surveyor’s individual judgement
considering the measurement conditions.
The Least Squares method is a rigorous
technique that is founded upon
probabilistic theory.
It requires an over-determined solution
(redundant measurements) to compute
the best estimated position for each of the
traverse stations.
29
Adjustments –Transit Rule
The transit rule applies adjustments
proportional to the size of the easting or
northing component between two stations
and the sum of the easting and northing
differences.
Adjustments –Transit Rule
The transit rule applies adjustments
proportional to the size of the easting or
northing component between two stations
and the sum of the easting and northing
differences.
30
Example: Closed Traverse Computation
Measurements of traverse ABCDE are given
in Table 1. Given that the co-ordinates of A
are 782.820mE, 460.901mN; and co -
ordinates of E are 740.270mE, 84.679mN.
The WCB of XA is 123-17-08 and WCB of EY
is 282-03-00.
Example: Closed Traverse Computation
Measurements of traverse ABCDE are given
in Table 1. Given that the co-ordinates of A
are 782.820mE, 460.901mN; and co -
ordinates of E are 740.270mE, 84.679mN.
The WCB of XA is 123-17-08 and WCB of EY
is 282-03-00.
31
Example: Traverse Computation (con’t)
a)Determine the angular, easting, northingand
linear misclosureof the traverse.
b)Calculateand tabulatethe adjusted co-
ordinates for B, C and D using Bowditch Rule.StationClockwise angleLength (m)
A 260-31-18
B 123-50-42 129.352
C 233-00-06 81.700
D 158-22-48 101.112
E 283-00-18 94.273
Example: Traverse Computation (con’t)
a)Determine the angular, easting, northingand
linear misclosureof the traverse.
b)Calculateand tabulatethe adjusted co-
ordinates for B, C and D using Bowditch Rule.StationClockwise angleLength (m)
A 260-31-18
B 123-50-42 129.352
C 233-00-06 81.700
D 158-22-48 101.112
E 283-00-18 94.273
32
Example: Traverse Computation (con’t)
1)There is no need to calculate the starting
and ending bearings as they are given.
2)Calculate the angular misclosure and
angular correction using:
F’=
I+ sum of angles -(n x 180)
Example: Traverse Computation (con’t)
1)There is no need to calculate the starting
and ending bearings as they are given.
2)Calculate the angular misclosure and
angular correction using:
F’=
I+ sum of angles -(n x 180)
33
Example: Traverse Computation (con’t)
F’=
I+sumofangles-(nx180)
sumofangles
=(260-31-18)+(123-50-42)+(233-00-06)+
(158-22-48)+(283-00-18)=(1058-45-12)
I=123-17-08; (nx180)=900
F’= (123-17-08) + (1058-45-12) -900 = 282-
02-20
angular misc.= (282-02-20) -(282-03-00) = -
40”
As there are five angles, each will be added
by the following factor of (40”/5) = 8”.
Example: Traverse Computation (con’t)
F’=
I+sumofangles-(nx180)
sumofangles
=(260-31-18)+(123-50-42)+(233-00-06)+
(158-22-48)+(283-00-18)=(1058-45-12)
I=123-17-08; (nx180)=900
F’= (123-17-08) + (1058-45-12) -900 = 282-
02-20
angular misc.= (282-02-20) -(282-03-00) = -
40”
As there are five angles, each will be added
by the following factor of (40”/5) = 8”.
34
Example: Closed Traverse
Computation (con’t)
Angular correction:
AX 303-17-08
A 260-31-18
(+8”)
563-48-34
360-00-00
A to B 203-48-34
180-00-00
B to A 23-48-34
B 123-50-42(+8”)
B to C 147-39-24
180-00-00
C to B 327-39-24
C 233-00-
06(+8”)
560-39-38
360-00-00
C to D 200-39-38
Example: Closed Traverse
Computation (con’t)
Angular correction:
AX 303-17-08
A 260-31-18
(+8”)
563-48-34
360-00-00
A to B 203-48-34
180-00-00
B to A 23-48-34
B 123-50-42(+8”)
B to C 147-39-24
180-00-00
C to B 327-39-24
C 233-00-
06(+8”)
560-39-38
360-00-00
C to D 200-39-38
35
Example: Closed Traverse
Computation (con’t)
C to D 200-39-38
180-00-00
D to C 20-39-38
D 158-22-
48(+8”)
D to E 179-02-34
180-00-00
E to D 359-02-34
E 283-00-
18(+8”)
642-03-00
360-00-00
E to Y282-03-00
(checks)
Example: Closed Traverse
Computation (con’t)
C to D 200-39-38
180-00-00
D to C 20-39-38
D 158-22-
48(+8”)
D to E 179-02-34
180-00-00
E to D 359-02-34
E 283-00-
18(+8”)
642-03-00
360-00-00
E to Y282-03-00
(checks)
36
Example: Closed Traverse
Computation (con’t)
Set up table and fill in bearings, distances,
starting and ending bearings. Calculate
the total traversed distance.Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352
C 147-39-2481.700
D 200-39-38101.112
E 179-02-3494.273 84.679740.270
406.437 84.679740.270
-460.901-782.820
-376.222-42.550
Example: Closed Traverse
Computation (con’t)
Set up table and fill in bearings, distances,
starting and ending bearings. Calculate
the total traversed distance.Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352
C 147-39-2481.700
D 200-39-38101.112
E 179-02-3494.273 84.679740.270
406.437 84.679740.270
-460.901-782.820
-376.222-42.550
37
Example: Closed Traverse
Computation (con’t)
For each leg, calculate N[Dist *
cos(Brg)] & E[Dist * sin(Brg)]. Sum N
and E. Compare results with diff.
between start and end coords.Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352-118.343-52.219
C 147-39-2481.700 -69.025 43.709
D 200-39-38101.112 -94.609 -35.675
E 179-02-3494.273 -94.260 1.575
406.437-376.237-42.610 84.679740.270
-460.901-782.820
-376.222-42.550
Example: Closed Traverse
Computation (con’t)
For each leg, calculate N[Dist *
cos(Brg)] & E[Dist * sin(Brg)]. Sum N
and E. Compare results with diff.
between start and end coords.Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352-118.343-52.219
C 147-39-2481.700 -69.025 43.709
D 200-39-38101.112 -94.609 -35.675
E 179-02-3494.273 -94.260 1.575
406.437-376.237-42.610 84.679740.270
-460.901-782.820
-376.222-42.550
38
Example: Closed Traverse
Computation (con’t)
Compute the error in eastings , northings
and linear misclosure
error in Eastings = -42.610 -(-42.550) = -
0.060m
error in Northings = -376.237 -(-376.222)
= -0.015m
Linear misclosure
= (((-0.060)
2
+ (-0.015)
2
)
0.5
) / 406.437
= 0.062 / 406.437 = 1 / 6555
Example: Closed Traverse
Computation (con’t)
Compute the error in eastings , northings
and linear misclosure
error in Eastings = -42.610 -(-42.550) = -
0.060m
error in Northings = -376.237 -(-376.222)
= -0.015m
Linear misclosure
= (((-0.060)
2
+ (-0.015)
2
)
0.5
) / 406.437
= 0.062 / 406.437 = 1 / 6555
39
Example: Closed Traverse
Computation (con’t)
Using Bowditch Rule, calculate correction
for each N & E. ((partial dist./total
dist.) * (error in N or E)Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352-118.343
+0.005
-52.219
+0.020
C 147-39-2481.700 -69.025
+0.003
43.709
+0.012
D 200-39-38101.112 -94.609
+0.004
-35.675
+0.014
E 179-02-3494.273 -94.260
+0.003
1.575
+0.014
406.437-376.237-42.610 84.679740.270
-460.901-782.820
-376.222-42.550
Example: Closed Traverse
Computation (con’t)
Using Bowditch Rule, calculate correction
for each N & E. ((partial dist./total
dist.) * (error in N or E)Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352-118.343
+0.005
-52.219
+0.020
C 147-39-2481.700 -69.025
+0.003
43.709
+0.012
D 200-39-38101.112 -94.609
+0.004
-35.675
+0.014
E 179-02-3494.273 -94.260
+0.003
1.575
+0.014
406.437-376.237-42.610 84.679740.270
-460.901-782.820
-376.222-42.550
40
Example: Closed Traverse
Computation (con’t)
Final coordinates of station= coords. of
previous station + partial coords () +
corr.Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352-118.343
+0.005
-52.219
+0.020
342.563730.621
C 147-39-2481.700 -69.025
+0.003
43.709
+0.012
273.541774.342
D 200-39-38101.112 -94.609
+0.004
-35.675
+0.014
178.936738.681
E 179-02-3494.273 -94.260
+0.003
1.575
+0.014
84.679740.270
406.437-376.237-42.610 84.679740.270
-460.901-782.820
-376.222-42.550
Example: Closed Traverse
Computation (con’t)
Final coordinates of station= coords. of
previous station + partial coords () +
corr.Sta. Brg Dist N E N E
A 460.901782.820
B 203-48-34129.352-118.343
+0.005
-52.219
+0.020
342.563730.621
C 147-39-2481.700 -69.025
+0.003
43.709
+0.012
273.541774.342
D 200-39-38101.112 -94.609
+0.004
-35.675
+0.014
178.936738.681
E 179-02-3494.273 -94.260
+0.003
1.575
+0.014
84.679740.270
406.437-376.237-42.610 84.679740.270
-460.901-782.820
-376.222-42.550
ERROR PROPAGATION IN
TRAVERSE SURVEYS
41
TRAVERSE SURVEYS
41
Eventhoughthespecificationsforaprojectmayallowloweraccuracies,
thepresenceofblundersinobservationsisneveracceptable.
Thus,animportantquestionforeverysurveyoris:HowcanItellwhen
blundersarepresentinthedata?
Generally,observationsinhorizontalsurveys(e.g.,traverses)are
independent.Thatis,themeasurementofadistanceobservationis
independentoftheazimuthobservation.Butthelatitudeanddeparture
ofaline,whicharecomputedfromthedistanceandazimuth
observations,arenotindependent.
42
thepresenceofblundersinobservationsisneveracceptable.
Thus,animportantquestionforeverysurveyoris:HowcanItellwhen
blundersarepresentinthedata?
Generally,observationsinhorizontalsurveys(e.g.,traverses)are
independent.Thatis,themeasurementofadistanceobservationis
independentoftheazimuthobservation.Butthelatitudeanddeparture
ofaline,whicharecomputedfromthedistanceandazimuth
observations,arenotindependent.
42
Thefollowingfigureshowstheeffectsoferrorsindistanceandazimuth
observationsonthecomputedlatitudeanddeparture.Inthefigureitcanbe
seenthatthereiscorrelationbetweenthelatitudeanddeparture;thatis,if
eitherdistanceorazimuthobservationchanges,itcauseschangesinboth
latitudeanddeparture.
43
observationsonthecomputedlatitudeanddeparture.Inthefigureitcanbe
seenthatthereiscorrelationbetweenthelatitudeanddeparture;thatis,if
eitherdistanceorazimuthobservationchanges,itcauseschangesinboth
latitudeanddeparture.
43
DERIVATION OF ESTIMATED ERROR IN LATITUDE
AND DEPARTURE
44
AND DEPARTURE
44
The estimated errors in these values are solved using matrix Equation as
45
45
propagationofobservationalerrorsthroughtraversecomputationshasbeen
discussed.
Errorpropagationisapowerfultoolforthesurveyor,enablingananswerto
beobtainedforthequestion:Whatisanacceptabletraversemisclosure?
Thisisanexampleofsurveyingengineering.
Surveyorsareconstantlydesigningmeasurementsystemsandchecking
theirresultsagainstpersonalorlegalstandards.Thesubjectsoferror
propagationanddetectionofmeasurementblundersarediscussedfurther
inlaterchapters.
46
discussed.
Errorpropagationisapowerfultoolforthesurveyor,enablingananswerto
beobtainedforthequestion:Whatisanacceptabletraversemisclosure?
Thisisanexampleofsurveyingengineering.
Surveyorsareconstantlydesigningmeasurementsystemsandchecking
theirresultsagainstpersonalorlegalstandards.Thesubjectsoferror
propagationanddetectionofmeasurementblundersarediscussedfurther
inlaterchapters.
46
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