Transcript Slide 1

Introduction to Traversing
Traversing is the method of using distances and directions of lines
between
points to
determine positions of the points.
D
C
E
Example of Typical traverse
F
Types of Traverses
I. Loop Traverse
Distance and angles
measured
II. Link Traverse
Types of Link Traverses
B
A
D
C
E
F
G
H
Special case of the traverse
Typical sequence of computing
Procedures
1. Adjustment of Angles
2. Compute Azimuths
3. Adjustment of distances (Latitudes and Departures)
4. Compute Coordinates
A
1 orientation point
Left angle B
Orientation Point
with known X,Y
Left angle
1
1
Traverse leg d1-2
1
dB-1
B
2 orientation point
Compute direction
d1-2
2
Traverse Station
with unknown X,Y
1. Adjustment of Angles
Adjustment of Angles in a Loop Traverse
B
Check Interior Angle Closure
Observed
A
B
C
D
E
Total =
5390
59’ 00” =
1490 13’00”
Adjusted
= 1010 24’ 00”
= 1490 13’ 00”
= 800 58’ 30”
= 1160 19’ 00”
= 920 04’ 30”
1010 24’ 12”
1490 13’ 12”
800 58’ 42”
1160 19’ 12”
920 04’ 42”
5400
00’ 00”
Should = 5400 00’ 00” = (n-2)*180
Misclosure = 01’ 00” = 60”
Adjustment = 60/5 = +12” per angle
C
A
1010 24’00”
D
E
1.Compute Azimuths
Ap

A
An
B
Ap
180

An = Ap +  – 180
An = Ap –  + 180
Compute next azimuths An
1
1.Compute Azimuths
Compute Azimuths in Loop traverse
AB
BA
B
BC
CB
C
CD
DC
D
DE
ED
E
EA
AE
A
AB
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
510 22’ 00” (given)
2310 22’ 00”
1490 13’ 12”
820 08’ 48”
2620 08’ 48”
800 58’ 42”
1810 10’ 06”
10 10’ 06”
1160 19’ 12”
2440 50’ 54”
640 50’ 54”
920 04’ 42”
3320 46’ 12”
1520 46’ 12”
1010 24’ 12”
510 22’ 00” Check
B
82° 08’ 48”
C
1490 13’12”
A
1010 24’12”
D
E
AB-1 = AAB+B – 180
A1-2 = AB-1+1 – 180
A2-3 = A1-2+2 – 180
A3-C = A2-3+3 – 180
ACD = A3-C+C – 180
ACD = AAB+ [left ] – n180
ACD = AAB - [right ] +
n180
1. Adjustment of Angles
II. Link Traverse
[left] = AK – AP + n180
[right ] = AP – AK + n180
B
2
A
B
dB-1
C
3
2
1
d1-2
d2-3
d3-C
C
3
1
Diredctin of the calculations
D
Bilateral traverse typical
Adjustment of Angles in a Link Traverse
Should = AK – AP + n 180 or (AP – AK + n180 )
Misclosure = [  left ] – (AK – AP + n 180 )
or
[ right ] - (AP – AK + n180 )
1. Adjustment of Angles
Adjustment of Angles in a Link Traverse
D
C
E
F
Sum angles Should be = AK – AP + n 180 or AP – AK + n180
Misclosure = [ angles left ] – (AK – AP + n 180 )
or
[angles right ] - (AP – AK + n180 )
Correction to angles = - Misclosure /number of angles
1.Compute Azimuths
O1
Link (open) Traverse
Traverse Station
with unknown X,Y
Traverse Terminal
with known X,Y
Orientation Point
with known X,Y
T1
T3
B
T2
A
T4
Abstract of Observations
From
A
A
A
T1
T1
T2
T2
T3
T3
T4
T4
B
B
B
To
O1
O1
T1
A
T2
T1
T3
T2
T4
T3
B
T4
O2
O2
Deg
355
355
75
255
110
290
80
260
111
291
82
262
170
Min
40
40
20
20
36
36
22
22
25
25
25
25
26
Sec
45
40
30
42
42
40
26
30
29
24
20
26
20
Prov.
Azimuth
Orient
Azimuth
Orient Prov. Oriented Corrn
Adjusted
Corrn Deg Min Sec
Deg Min Sec
5
5
-7
-7
-5
-5
-9
-9
-4
-4
-10
-10
Orientation Misclosure
355
75
40
20
45
35
1
75
20
36
110
36
35
2
110
36
37
80
22
21
3
80
22
24
111
25
20
4
111
25
24
82
25
16
5
82
25
21
170
170
0
26
26
0
10
15
-5
O2
O2
Latitudes (DY) and Departures (DX)
Latitude = L Cos  = DY
Departure = L Sin  = DX
DX
T2
DY

L
T1
Latitudes and Departures computed for each leg of a traverse
Adjustment of distances (Lats and Deps)
Compute Lats (D Cos ) and Deps (D Sin )
Leg
AB
BC
CD
DE
EA
Azimuth
510 22’ 00”
820 08’ 48”
1810 10’ 06”
2440 50’ 54”
3320 46’ 12”
Distance
401.58
382.20
368.28
579.03
350.10
Lat
Dep
250.720 313.697
52.222 378.615
-368.203
-7.509
-246.097 -524.130
311.301 -160.193
Total
-0.057
Total Traverse Distance = 2081.19
Linear Misclosure = (0.057)2 + (0.480)2 = 0.483
Precision = 0.483/2081.19 = 1/4305 …… 1/4300
0.480
Adjustment of distances (Lats and Deps)
Correction to Lats =
-
Traverse leg distance * Lat Misclosure
Total traverse distance
Correction to Deps =
-
Traverse leg distance * Dep Misclosure
Total traverse distance
Leg
AB
BC
CD
DE
EA
Lats
Deps
Corrn Lat
250.720
313.697
0.011
52.222
378.615
0.010
-368.203
-7.509
0.010
-246.097 -524.130
0.016
311.301 -160.193
0.010
Total
0.057
Corrn Dep
-0.093
-0.088
-0.085
-0.134
-0.081
-0.481
Adj Lats
250.731
52.232
-368.193
-246.081
311.311
0.000
Adj Deps
313.604
378.527
-7.594
-524.264
-160.274
0.001