2. Traverse
Traverse
consists of a series of straight lines connecting successive points whose
consists of a series of straight lines connecting successive points whose
lengths and directions have been determined from field observations
lengths and directions have been determined from field observations
points defining the ends of traverse lines are called traverse stations or
points defining the ends of traverse lines are called traverse stations or
traverse points
traverse points
4. Purpose of Traverse
Purpose of Traverse
1. Property surveys to locate or establish boundaries.
1. Property surveys to locate or establish boundaries.
2. Supplementary horizontal control for topographic mapping surveys.
2. Supplementary horizontal control for topographic mapping surveys.
3. Location and construction layout surveys for highways, railways and
3. Location and construction layout surveys for highways, railways and
other private and public works.
other private and public works.
4. Ground control surveys for photogrammetric surveys
4. Ground control surveys for photogrammetric surveys
5. Traverse Computation
Traverse Computation
In dealing with a closed traverse, we have computations in:
In dealing with a closed traverse, we have computations in:
1) Determining latitudes and departures
1) Determining latitudes and departures
2) Calculating total error of closure
2) Calculating total error of closure
3) Balancing the survey
3) Balancing the survey
4) Determining adjusted positions of traverse stations
4) Determining adjusted positions of traverse stations
5) Area computation
5) Area computation
6) Area subdivision
6) Area subdivision
6. Latitude and Departure
Latitude and Departure
LATITUDE
LATITUDE
Projection of a line onto a reference
Projection of a line onto a reference
meridian or North-South line
meridian or North-South line
Lines with Northerly bearings (+) LAT
Lines with Northerly bearings (+) LAT
Lines with Southerly bearings (-) LAT
Lines with Southerly bearings (-) LAT
Equal to distance*cosine of bearing angle
Equal to distance*cosine of bearing angle
7. Latitude and Departure
Latitude and Departure
DEPARTURE
DEPARTURE
Projection of a line onto a reference
Projection of a line onto a reference
parallel or East-West line
parallel or East-West line
Lines with Easterly bearings (+) DEP
Lines with Easterly bearings (+) DEP
Lines withWesterly bearings (-) DEP
Lines withWesterly bearings (-) DEP
Equal to distance*sine of bearing angle
Equal to distance*sine of bearing angle
8. Error of Closure
Error of Closure
Is usually a short line of unknown length and direction connecting the
Is usually a short line of unknown length and direction connecting the
initial and final traverse stations
initial and final traverse stations
Note: In computing for
Note: In computing for θ
θ, use the absolute values for
, use the absolute values for Σ
ΣDep and
Dep and Σ
ΣLat. Determine
Lat. Determine
the quadrant where the line falls using corresponding signs of the 2 sums
the quadrant where the line falls using corresponding signs of the 2 sums
9. Relative Error of Closure
Relative Error of Closure
Ratio of the linear error of closure to the perimeter or total length of the
Ratio of the linear error of closure to the perimeter or total length of the
traverse
traverse
REC = Relative Error of Closure
REC = Relative Error of Closure
LEC = Linear Error of Closure
LEC = Linear Error of Closure
D = Total Length or perimeter of the traverse
D = Total Length or perimeter of the traverse
10. Traverse Adjustments
Traverse Adjustments
Methods of adjustment are usually classified as:
Methods of adjustment are usually classified as:
I. Rigorous
I. Rigorous
Least Squares Method
Least Squares Method
II. Approximate
II. Approximate
Compass Rule (or Bowditch Rule)
Compass Rule (or Bowditch Rule)
Transit Rule
Transit Rule
Crandall Method
Crandall Method
11. Compass Rule
Compass Rule
Named after the distinguished American navigator Nathaniel Bowditch
Named after the distinguished American navigator Nathaniel Bowditch
(1773-1838)
(1773-1838)
Based on the assumption that:
Based on the assumption that:
1. All lengths are measured with equal care
1. All lengths are measured with equal care
2. All angles are taken with approximately the same precision
2. All angles are taken with approximately the same precision
3. Errors are accidental
3. Errors are accidental
4. Total error in any side is directly proportional to the length
4. Total error in any side is directly proportional to the length
of the traverse
of the traverse
12. Compass Rule
Compass Rule
Where;
Where;
c
clat
lat = correction to latitude
= correction to latitude
c
cdep
dep= correction to departure
= correction to departure
C
CL
L= total closure in lat =
= total closure in lat = Σ
Σ Lat
Lat
C
CD
D= total closure in dep=
= total closure in dep= Σ
Σ Dep
Dep
d = length of any course
d = length of any course
D = total length of the traverse
D = total length of the traverse
13. Compass Rule
Compass Rule
No sound theoretical foundation since it is purely empirical
No sound theoretical foundation since it is purely empirical
Not commonly used but best suited for surveys where traverse sides are
Not commonly used but best suited for surveys where traverse sides are
measured by stadia or subtensed bar method
measured by stadia or subtensed bar method
Based on the assumption that:
Based on the assumption that:
1. Angular measurements are more precise than linear
1. Angular measurements are more precise than linear measurements
measurements
2. Errors in traversing are accidental
2. Errors in traversing are accidental
Not applicable in some instances (lines in E ,W, N or S)
Not applicable in some instances (lines in E ,W, N or S)
14. Transit Rule
Transit Rule
Where:
Where:
c
clat
lat = correction to latitude
= correction to latitude
cd
cdep
ep= correction to departure
= correction to departure
CL= total closure in lat =
CL= total closure in lat = Σ
Σ Lat
Lat
CD= total closure in dep=
CD= total closure in dep= Σ
ΣDep
Dep
15. Example ( Traverse
Example ( Traverse
Adjustment)
Adjustment)
For the tabulated traverse below, compute for the following:
For the tabulated traverse below, compute for the following:
1. Latitude and Departure of each line
1. Latitude and Departure of each line
2. Bearing of the side error, LEC, REC
2. Bearing of the side error, LEC, REC
3. Adjust the traverse and compute for the adjusted coordinates of traverse stations
3. Adjust the traverse and compute for the adjusted coordinates of traverse stations
using Compass Rule
using Compass Rule
4. Adjust the traverse and compute for the adjusted coordinates of traverse stations
4. Adjust the traverse and compute for the adjusted coordinates of traverse stations
using using Transit Rule
using using Transit Rule
5. Provide a sketch of the traverse
5. Provide a sketch of the traverse
Note: Coordinates of A are
NA=20,000.000, EA=20,000.000
16. Example ( Solution)
Example ( Solution)
1. Latitude and Departure of each line
1. Latitude and Departure of each line
17. Example ( Solution)
Example ( Solution)
1. Latitude and Departure of each line
1. Latitude and Departure of each line
18. Example ( Solution)
Example ( Solution)
2
2. Bearing of the side error, LEC, REC
. Bearing of the side error, LEC, REC
Bearing of the side error:
Bearing of the side error:
Bearing of the side error is S 47
Bearing of the side error is S 47o
o
05’ W
05’ W
19. Example ( Solution)
Example ( Solution)
2
2. Bearing of the side error, LEC, REC
. Bearing of the side error, LEC, REC
Bearing of the side error:
Bearing of the side error:
Linear Error of Closure (LEC):
Linear Error of Closure (LEC):
Relative Error of Closure (REC):
Relative Error of Closure (REC):
Bearing of the side error is S 47
Bearing of the side error is S 47o
o
05’ W
05’ W
LEC = 24.69 m
LEC = 24.69 m
REC = 1/200
REC = 1/200
20. Example ( Solution)
Example ( Solution)
3. Traverse Adjustment by Compass Rule
3. Traverse Adjustment by Compass Rule
21. Example ( Solution)
Example ( Solution)
3. Traverse Adjustment by Compass Rule
3. Traverse Adjustment by Compass Rule
22. Example ( Solution)
Example ( Solution)
3. Traverse Adjustment by Compass Rule
3. Traverse Adjustment by Compass Rule
23. Example ( Solution)
Example ( Solution)
3. Traverse Adjustment by Compass Rule
3. Traverse Adjustment by Compass Rule
24. Example ( Solution)
Example ( Solution)
3. Traverse Adjustment by Compass Rule
3. Traverse Adjustment by Compass Rule
25. Example ( Solution)
Example ( Solution)
4. Traverse Adjustment by Transit Rule
4. Traverse Adjustment by Transit Rule
26. Example ( Solution)
Example ( Solution)
4. Traverse Adjustment by Transit Rule
4. Traverse Adjustment by Transit Rule
27. Example ( Solution)
Example ( Solution)
4. Traverse Adjustment by Transit Rule
4. Traverse Adjustment by Transit Rule
